Edgar Filing: FIRST TRUST ENERGY INFRASTRUCTURE FUND

UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

FORM N-CSR

CERTIFIED SHAREHOLDER REPORT OF REGISTERED MANAGEMENT INVESTMENT
COMPANIES

Investment Company Act file number 811-22528
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First Trust Energy Infrastructure Fund
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(Exact name of registrant as specified in charter)

120 East Liberty Drive, Suite 400
Wheaton, IL 60187
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(Address of principal executive offices) (Zip code)

W. Scott Jardine, Esq.
First Trust Portfolios L.P.
120 East Liberty Drive, Suite 400
Wheaton, IL 60187
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(Name and address of agent for service)

registrant's telephone number, including area code: 630-765-8000
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Date of fiscal year end: November 30
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Date of reporting period: November 30, 2012
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Form N-CSR is to be used by management investment companies to file reports with
the Commission not later than 10 days after the transmission to stockholders of
any report that is required to be transmitted to stockholders under Rule 30e-1
under the Investment Company Act of 1940 (17 CFR 270.30e-1). The Commission may
use the information provided on Form N-CSR in its regulatory, disclosure review,
inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-CSR,
and the Commission will make this information public. A registrant is not
required to respond to the collection of information contained in Form N-CSR
unless the Form displays a currently valid Office of Management and Budget
("OMB") control number. Please direct comments concerning the accuracy of the
information collection burden estimate and any suggestions for reducing the
burden to Secretary, Securities and Exchange Commission, 100 F Street, NE,
Washington, DC 20549. The OMB has reviewed this collection of information under
the clearance requirements of 44 U.S.C. ss. 3507.

ITEM 1. REPORTS TO STOCKHOLDERS.

The Report to Shareholders is attached herewith.

FIRST TRUST
ENERGY INFRASTRUCTURE
FUND

ANNUAL REPORT
For the Year Ended
November 30, 2012

First Trust

Energy Income Partners, LLC

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TABLE OF CONTENTS
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FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
ANNUAL REPORT
NOVEMBER 30, 2012

Shareholder Letter..................................................... 1
At A Glance............................................................ 2
Portfolio Commentary................................................... 3
Portfolio of Investments............................................... 6
Statement of Assets and Liabilities.................................... 10
Statement of Operations................................................ 11
Statement of Changes in Net Assets..................................... 12
Statement of Cash Flows................................................ 13
Financial Highlights................................................... 14
Notes to Financial Statements.......................................... 15
Report of Independent Registered Public Accounting Firm................ 22
Additional Information................................................. 23
Board of Trustees and Officers......................................... 25
Privacy Policy......................................................... 27

CAUTION REGARDING FORWARD-LOOKING STATEMENTS

This report contains certain forward-looking statements within the meaning of
the Securities Act of 1933, as amended, and the Securities Exchange Act of 1934,
as amended. Forward-looking statements include statements regarding the goals,
beliefs, plans or current expectations of First Trust Advisors L.P. ("First
Trust" or the "Advisor") and/or Energy Income Partners, LLC ("EIP" or the
"Sub-Advisor") and their respective representatives, taking into account the
information currently available to them. Forward-looking statements include all
statements that do not relate solely to current or historical fact. For example,
forward-looking statements include the use of words such as "anticipate,"
"estimate," "intend," "expect," "believe," "plan," "may," "should," "would" or
other words that convey uncertainty of future events or outcomes.

Forward-looking statements involve known and unknown risks, uncertainties and
other factors that may cause the actual results, performance or achievements of
the First Trust Energy Infrastructure Fund (the "Fund") to be materially
different from any future results, performance or achievements expressed or
implied by the forward-looking statements. When evaluating the information
included in this report, you are cautioned not to place undue reliance on these
forward-looking statements, which reflect the judgment of the Advisor and/or
Sub-Advisor and their respective representatives only as of the date hereof. We
undertake no obligation to publicly revise or update these forward-looking
statements to reflect events and circumstances that arise after the date hereof.

PERFORMANCE AND RISK DISCLOSURE

There is no assurance that the Fund will achieve its investment objective. The
Fund is subject to market risk, which is the possibility that the market values
of securities owned by the Fund will decline and that the value of the Fund
shares may therefore be less than what you paid for them. Accordingly, you can
lose money by investing in the Fund. See "Risk Considerations" in the Notes to
Financial Statements for a discussion of certain other risks of investing in the
Fund.

Performance data quoted represents past performance, which is no guarantee of
future results, and current performance may be lower or higher than the figures
shown. For the most recent month-end performance figures, please visit
http://www.ftportfolios.com or speak with your financial advisor. Investment
returns, net asset value and common share price will fluctuate and Fund shares,
when sold, may be worth more or less than their original cost.

HOW TO READ THIS REPORT

This report contains information that may help you evaluate your investment. It
includes details about the Fund and presents data and analysis that provide
insight into the Fund's performance and investment approach.

By reading the portfolio commentary by the portfolio management team of the
Fund, you may obtain an understanding of how the market environment affected the
Fund's performance. The statistical information that follows may help you
understand the Fund's performance compared to that of relevant market
benchmarks.

It is important to keep in mind that the opinions expressed by personnel of EIP
are just that: informed opinions. They should not be considered to be promises
or advice. The opinions, like the statistics, cover the period through the date
on the cover of this report. The risks of investing in the Fund are spelled out
in the prospectus, the statement of additional information, this report and
other Fund regulatory filings.

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SHAREHOLDER LETTER
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FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
ANNUAL LETTER FROM THE CHAIRMAN AND CEO
NOVEMBER 30, 2012

Dear Shareholders:

I am pleased to present you with the annual report for your investment in First
Trust Energy Infrastructure Fund (the "Fund").

The report you hold contains detailed information about your investment; a
portfolio commentary from the Fund's management team that provides a recap of
the period; a performance analysis and a market and Fund outlook. Additionally,
you will find the Fund's financial statements for the period this report covers.
I encourage you to read this document and discuss it with your financial
advisor. A successful investor is also typically a knowledgeable one, as we have
found to be the case at First Trust.

First Trust remains committed to being a long-term investor and investment
manager and to bringing you quality financial solutions regardless of market ups
and downs. We have always believed, as I have written previously, that there are
two ways to attain success in reaching your financial goals: staying invested in
quality products and having a long-term investment horizon. We are committed to
this approach in the products we manage or supervise and offer to investors.

As you know, First Trust offers a variety of products that we believe could fit
many financial plans to help investors seeking long-term investment success. We
encourage you to talk to your advisor about the other investments First Trust
offers that might also fit your financial goals and to discuss those goals with
your advisor regularly so that he or she can help keep you on track.

First Trust will continue to make available up-to-date information about your
investments so you and your financial advisor are current on any First Trust
investments you own. We value our relationship with you, and thank you for the
opportunity to assist you in achieving your financial goals. I look forward to
the New Year and to the next edition of your Fund's report.

Sincerely,

/s/ James A. Bowen

James A. Bowen
Chairman of the Board of Trustees of First Trust Energy Infrastructure Fund and
Chief Executice Officer of First Trust Advisors L.P.

Page 1

FIRST TRUST ENERGY INFRASTRUCTURE FUND
"AT A GLANCE"
AS OF NOVEMBER 30, 2012 (UNAUDITED)

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FUND STATISTICS
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Symbol on New York Stock Exchange FIF
Common Share Price $21.34
Common Share Net Asset Value ("NAV") $22.74
Premium (Discount) to NAV (6.16)%
Net Assets Applicable to Common Shares $399,091,735
Current Monthly Distribution per Common Share (1) $0.1085
Current Annualized Distribution per Common Share $1.3020
Current Distribution Rate on Closing Common Share Price (2) 6.10%
Current Distribution Rate on NAV (2) 5.73%
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COMMON SHARE PRICE & NAV (WEEKLY CLOSING PRICE)
------------------------------------------------

Common Share Price NAV
11/11 $19.80 $21.43
20.00 21.37
20.05 21.34
20.35 22.35
12/11 20.25 22.47
21.08 22.31
20.83 21.95
20.78 22.19
1/12 21.08 22.22
21.15 22.39
21.36 22.45
21.49 22.76
2/12 21.74 22.94
21.96 22.92
21.63 22.93
21.80 22.57
21.16 22.56
3/12 21.29 22.52
21.25 22.55
20.75 22.10
20.97 22.55
4/12 21.63 23.03
21.18 22.67
21.15 22.60
19.94 21.66
5/12 20.26 22.16
20.09 21.25
20.19 21.69
19.97 21.62
19.98 21.61
6/12 20.85 22.35
20.96 22.51
21.43 22.95
21.60 23.25
712 21.69 23.38
21.80 23.32
21.74 23.30
22.04 23.44
22.00 23.16
8/12 21.86 23.09
21.89 23.20
22.25 23.41
22.11 23.38
9/12 22.10 23.52
22.25 23.84
21.70 23.44
22.00 23.63
10/12 21.67 23.29
21.47 23.08
20.62 22.12
20.60 21.67
20.64 22.33
11/12 21.34 22.74

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PERFORMANCE
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Average Annual Total Return
---------------------------
Inception
1 Year Ended (9/27/2011)
11/30/2012 to 11/30/2012

Fund Performance (3)
NAV 13.08% 22.21%
Market Value 14.47% 11.33%

Index Performance
Philadelphia Stock Exchange Utility Index 3.08% 5.76%
Alerian MLP Total Return Index 14.40% 19.22%
Blended Benchmark (4) 8.74% 12.49%
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% OF TOTAL
INDUSTRY CLASSIFICATION INVESTMENTS
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Pipelines 56.8%
Electric Power 32.3
Propane 5.4
Marine 2.2
Coal 1.7
Other 1.6
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Total 100.0%
======

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% OF TOTAL
TOP 10 HOLDINGS INVESTMENTS
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Kinder Morgan Management, LLC 7.2%
Enbridge Energy Management, LLC 6.7
Dominion Resources, Inc. 4.1
Southern Co. 4.1
NextEra Energy, Inc. 3.6
Williams Cos., Inc. 3.5
NiSource, Inc. 3.4
Duke Energy Corp. 3.2
TransCanada Corp. 3.2
Centerpoint Energy, Inc. 3.0
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Total 42.0%
======

(1) Most recent distribution paid or declared through 11/30/2012.
Subject to change in the future.

(2) Distribution rates are calculated by annualizing the most recent
distribution paid or declared through the report date and then
dividing by Common Share price or NAV, as applicable, as of
11/30/2012. Subject to change in the future.

(3) Total return is based on the combination of reinvested dividend,
capital gain and return of capital distributions, if any, at
prices obtained by the Dividend Reinvestment Plan and changes in
NAV per share for NAV returns and changes in Common Share price
for market value returns. Total returns do not reflect sales load
and are not annualized for periods less than one year. Past
performance is not indicative of future results.

(4) The blended benchmark consists of the following: Philadelphia
Stock Exchange Utility Index (50%) and Alerian MLP Total Return
Index (50%).

Page 2

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PORTFOLIO COMMENTARY
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FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
ANNUAL REPORT
NOVEMBER 30, 2012

SUB-ADVISOR

ENERGY INCOME PARTNERS, LLC

Energy Income Partners, LLC ("EIP"), located in Westport, CT, was founded in
2003 to provide professional asset management services in the area of
energy-related master limited partnerships ("MLPs") and other high-payout
securities such as pipeline companies, power utilities and Canadian income
trusts and their successor companies (collectively, "Canadian Income Equities").
EIP mainly focuses on investments in energy-related infrastructure assets such
as pipelines, power transmission, petroleum storage and terminals that receive
fee-based or regulated income from their corporate customers. EIP manages or
supervises approximately $2.8 billion of assets, as of November 30, 2012. The
other funds advised by EIP include a partnership for U.S. high net worth
individuals and a master-and-feeder fund for institutions. EIP also manages
separately managed accounts. EIP is a registered investment advisor and serves
as a sub-advisor to two closed-end management investment companies other than
the Fund and an actively managed exchange-traded fund (ETF).

PORTFOLIO MANAGEMENT TEAM

JAMES J. MURCHIE
FOUNDER AND CEO OF ENERGY INCOME PARTNERS, LLC

Mr. Murchie founded EIP in 2003 and is the portfolio manager for all funds
advised by EIP which focus on energy-related master limited partnerships and
other high payout securities of companies that operate energy infrastructure.
From 2005 to mid-2006, Mr. Murchie and the EIP investment team joined Pequot
Capital Management. In July 2006, Mr. Murchie and the EIP investment team left
Pequot and re-established EIP. From 1998 to 2003, Mr. Murchie managed a
long/short fund that invested in energy and cyclical equities and commodities.
From 1995 to 1997, he was a managing director at Tiger Management where his
primary responsibilities were investments in energy, commodities and related
equities. From 1990 to 1995, Mr. Murchie was a principal at Sanford C. Bernstein
where he was a top-ranked energy analyst and sat on the Research Department's
Recommendation Review Committee. Before joining Bernstein, he spent eight years
at British Petroleum in seven operating and staff positions of increasing
responsibility. He has served on the board of Clark Refining and Marketing
Company and as President and Treasurer of the Oil Analysts Group of New York.
Mr. Murchie holds degrees from Rice University and Harvard University.

EVA PAO
PRINCIPAL OF ENERGY INCOME PARTNERS, LLC

Ms. Pao has been with EIP since its inception in 2003 and is co-portfolio
manager for all of the funds advised by EIP. She joined EIP in 2003, serving as
Managing Director of EIP until the EIP investment team joined Pequot Capital
Management. From 2005 to mid-2006, Ms. Pao served as Vice President of Pequot
Capital Management. Prior to Harvard Business School, Ms. Pao was a Manager at
Enron Corp where she managed a portfolio in Canadian oil and gas equities for
Enron's internal hedge fund that specialized in energy-related equities and
managed a natural gas trading book. She received a B.A. from Rice University in
1996 and an M.B.A. from the Harvard Business School in 2002.

FIRST TRUST ENERGY INFRASTRUCTURE FUND

The investment objective of the First Trust Energy Infrastructure Fund ("FIF" or
the "Fund") is to seek a high level of total return with an emphasis on current
distributions paid to shareholders. The Fund pursues its objective by investing
primarily in securities of companies engaged in the energy infrastructure
sector. These companies principally include publicly-traded master limited
partnerships ("MLPs"), MLP affiliates, Canadian Income Equities, pipeline
companies, utilities and other infrastructure related companies that derive at
least 50% of their revenues from operating or providing services in support of
infrastructure assets such as pipelines, power transmission and petroleum and
natural gas storage in the petroleum, natural gas and power generation
industries (collectively, "Energy Infrastructure Companies"). Under normal
market conditions, the Fund invests at least 80% of its managed assets (total
asset value of the Fund minus the sum of the Fund's liabilities other than the
principal amount of borrowing) in securities of Energy Infrastructure Companies.
There can be no assurance that the Fund's investment objective will be achieved.
The Fund may not be appropriate for all investors.

MARKET RECAP

As measured by the Alerian MLP Total Return Index ("AMZX") and the Philadelphia
Stock Exchange Utility Index ("UTY"), the total return for energy-related MLPs
and utilities over the fiscal year ended November 30, 2012 was 14.40% and 3.08%,
respectively. These figures are according to data collected from several
sources, including Alerian Capital Management and Bloomberg. While in the short

Page 3

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PORTFOLIO COMMENTARY - (CONTINUED)
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term, share appreciation of Energy Infrastructure Companies can be volatile, we
believe that over the longer term, share appreciation will approximate growth in
per share quarterly cash distributions and dividends. Over the last 10 years,
growth in per share MLP distributions and utility dividends has averaged 6.9%
and 6.0% respectively. Over the last 12 months, the cash distributions of MLPs
and utilities increased by about 6.6% and 2.0%, respectively (source: Alerian
Capital Management and Bloomberg).

PERFORMANCE ANALYSIS

On a net asset value ("NAV") basis, the Fund provided a total return(1) of
13.08%, including the reinvestment of dividends, for the fiscal year ended
November 30, 2012. This compares, according to collected data, to a total return
of 8.74% for the average of the two benchmarks (14.40% for the AMZX and 3.08%
for UTY). On a market value basis, the Fund had a total return, including the
reinvestment of dividends of 14.47%, for the fiscal year ended November 30,
2012. The Fund's discount to NAV narrowed over the course of the fiscal year. On
November 30, 2012, the Fund was priced at $21.34, while the NAV was $22.74, a
discount of 6.16%, while on November 30, 2011, the Fund was priced at $19.82,
while the NAV was $21.38, a discount of 7.30%.

The Fund declared regular monthly Common Share distributions of $0.1085 per
share for each month of the reporting period. The outperformance of the Fund's
NAV relative to the 8.74% average of the AMZX and UTY benchmarks was driven by
outperforming positions that made up a larger portion of the Fund than of the
respective benchmarks. The companies held by the Fund tended to have
non-cyclical and/or regulated businesses like pipelines, power transmission and
distribution and storage terminals, while the benchmarks included numerous
companies that operated businesses whose earnings and cash flows were more
cyclical. This approach had a favorable impact on performance relative to the
benchmarks over the reporting period.

An important factor that affected the return of the Fund was the Fund's use of
financial leverage through the use of a line of credit. The Fund has a committed
facility agreement with the Bank of Nova Scotia with a maximum commitment amount
of $145,000,000. The Fund uses leverage because its managers believe that, over
time, leverage can enhance total return for common shareholders. However, the
use of leverage can also increase the volatility of the NAV and therefore
volatility of the share price. For example, as the prices of securities held by
the Fund decline, the effect of changes in Common Share NAV and common
shareholder total return is magnified by the use of leverage, and conversely,
leverage may enhance Common Share returns during periods when the prices of
securities held by the Fund generally are rising. Unlike the Fund, AMZX and UTY
are not leveraged. Leverage had a positive impact on the performance of the Fund
over this reporting period.

MARKET AND FUND OUTLOOK

The MLP asset class experienced 12 IPOs in 2012, as of 11/30/12. There was also
a healthy level of secondary financing activity for MLPs during the reporting
period as MLPs continued to fund their ongoing investments in new pipelines,
processing and storage facilities. In 2012, there were 62 secondary equity
offerings for MLPs that raised $23.2 billion through November 30, 2012. This
compares to $12.2 billion raised in 2011. MLPs also found access to the public
debt markets, raising $16.1 billion in 21 offerings during the same time period.
This compares to $15.6 billion in 2011 (source: Barclays Capital). The
combination of equity and debt raised of approximately $39 billion represents
approximately 12% of the roughly $319 billion MLP market cap.

Capital spending for utilities continues to increase. As measured by the UTY,
capital expenditures for the power utility industry have grown from $34 billion
and $45 billion in 2002 and 2007, respectively, to $60 billion last year. This
growth in expenditures is in response to needs such as reliability,
interconnection, modernization and growing demand. These capital investments are
supported, in part, by federal and state regulation, which allows companies to
recoup investments made in their rate structure.

The Fund continues to aim to be invested in Energy Infrastructure Companies with
mostly non-cyclical cash flows, investment-grade ratings, conservative balance
sheets, modest and/or flexible organic growth commitments and liquidity on their
revolving lines of credit. Since the Fund invests in securities that tend to
have high dividend payout ratios (as measured versus earnings), securities with
unpredictable cyclical cash flows make them a poor fit with the portfolio, in
the opinion of the Sub-Advisor. While there are some businesses within the
Fund's portfolio whose cash flows are cyclical, they are usually small and
analysed in the context of each company's financial and operating leverage and
payout ratio.

MLPs continue to play an integral role in the restructuring of more diversified
energy conglomerates. This restructuring includes the creation by these more
diversified conglomerates of MLP subsidiaries that contain assets such as
pipelines and storage terminals. It also includes the divestiture by some of the
parent companies of most or all of their cyclical businesses, leaving the parent

(1) Total return is based on the combination of reinvested dividend, capital
gain and return of capital distributions, if any, at prices obtained by
the Dividend Reinvestment Plan and changes in NAV per share for NAV
returns and changes in Common Share price for market value returns. Total
returns do not reflect sales load and are not annualized for periods less
than one year. Past performance is not indicative of future results.

Page 4

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PORTFOLIO COMMENTARY - (CONTINUED)
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company looking very similar to an old-fashioned pipeline utility with a large
holding in a subsidiary MLP. Diversified energy conglomerates are doing this so
that their regulated infrastructure assets with predictable cash flows may be
better valued by the market, resulting in a better financing tool to raise
capital for the new energy infrastructure projects related to the rapid growth
of North American oil and gas production and the need to upgrade the power grid.

In the opinion of the Sub-Advisor, the total return proposition of owning
energy-related infrastructure MLPs has been and continues to be their yield plus
their growth in dividends. The yield of the MLPs, weighted by market
capitalization, on November 30, 2012, was 6.34% based on AMZX, and for
utilities, was 4.26%, as measured by the UTY. The growth in the quarterly cash
distributions that make up this yield has averaged 6.9% annually over the last
ten years for MLPs and 6.0% for utilities. While it is uncertain what these
growth rates will be in the future, in the opinion of the Sub-Advisor, growth
will continue to be driven by three factors: 1) modest increases in volume
growth from both demand for energy and increases in North American oil and gas
production, 2) inflation, cost escalators and cost pass-throughs in pipeline and
power transmission tariffs and contracts and 3) accretion from profitable
capital projects and acquisitions.

Page 5

FIRST TRUST ENERGY INFRASTRUCTURE FUND
PORTFOLIO OF INVESTMENTS
NOVEMBER 30, 2012

SHARES/
UNITS DESCRIPTION VALUE
------------ ----------------------------------------------------------------------------- --------------

COMMON STOCKS - 98.4%

ELECTRIC UTILITIES - 26.2%
263,266 Duke Energy Corp. (a)........................................................ $ 16,801,636
304,600 Emera, Inc. (CAD) (a)........................................................ 10,462,528
366,450 Exelon Corp. (a)............................................................. 11,074,119
109,800 Fortis, Inc. (CAD) (a)....................................................... 3,689,660
105,000 ITC Holdings Corp. (a)....................................................... 8,247,750
272,600 NextEra Energy, Inc. (a)..................................................... 18,730,346
365,800 Northeast Utilities (a)...................................................... 14,171,092
494,500 Southern Co. (a)............................................................. 21,535,475
--------------
104,712,606
--------------
GAS UTILITIES - 5.2%
1,600 ONEOK, Inc................................................................... 71,792
384,200 Questar Corp. (a)............................................................ 7,538,004
396,479 UGI Corp. (a)................................................................ 13,171,032
--------------
20,780,828
--------------
MULTI-UTILITIES - 20.8%
35,000 Atco, Ltd. (CAD) (a)......................................................... 2,683,093
45,500 Canadian Utilities, Ltd. (CAD) (a)........................................... 3,079,901
797,600 Centerpoint Energy, Inc. (a)................................................. 15,736,648
421,400 Dominion Resources, Inc. (a)................................................. 21,537,754
175,000 National Grid PLC, ADR (a)................................................... 9,912,000
745,400 NiSource, Inc. (a)........................................................... 18,016,318
75,000 Sempra Energy................................................................ 5,131,500
185,000 Wisconsin Energy Corp. (a)................................................... 6,943,050
--------------
83,040,264
--------------
OIL, GAS & CONSUMABLE FUELS - 46.2%
1,197,390 Enbridge Energy Management, LLC (a) (b)...................................... 35,323,005
474,600 Enbridge Income Fund Holdings, Inc. (CAD) (a)................................ 11,012,765
326,869 Enbridge, Inc. (a)........................................................... 13,169,552
182,300 Keyera Corp. (CAD) (a)....................................................... 8,733,736
499,732 Kinder Morgan Management, LLC (a) (b)........................................ 37,929,659
326,500 Kinder Morgan, Inc........................................................... 11,038,965
482,100 Pembina Pipeline Corp. (CAD) (a)............................................. 13,652,261
540,950 Spectra Energy Corp. (a)..................................................... 15,119,552
360,400 TransCanada Corp. (a)........................................................ 16,574,796
258,000 Veresen, Inc. (CAD) (a)...................................................... 3,293,341
560,700 Williams Cos., Inc. (a)...................................................... 18,413,388
--------------
184,261,020
--------------

TOTAL COMMON STOCKS.......................................................... 392,794,718
(Cost $366,724,601) --------------

MASTER LIMITED PARTNERSHIPS - 33.1%

GAS UTILITIES - 3.8%
252,764 AmeriGas Partners, L.P. (a).................................................. 10,284,967
125,000 Suburban Propane Partners, L.P. (a).......................................... 4,923,750
--------------
15,208,717
--------------

Page 6 See Notes to Financial Statements

FIRST TRUST ENERGY INFRASTRUCTURE FUND
PORTFOLIO OF INVESTMENTS - (CONTINUED)
NOVEMBER 30, 2012

SHARES/
UNITS DESCRIPTION VALUE
------------ ----------------------------------------------------------------------------- --------------

MASTER LIMITED PARTNERSHIPS - (CONTINUED)

OIL, GAS & CONSUMABLE FUELS - 29.3%
20,000 Alliance GP Holdings, L.P.................................................... $ 917,800
79,565 Alliance Resource Partners, L.P. (a)......................................... 4,524,862
162,000 El Paso Pipeline Partners, L.P. (a).......................................... 6,047,460
149,000 Energy Transfer Equity, L.P. (a)............................................. 6,775,030
91,600 Enterprise Products Partners, L.P. (a)....................................... 4,747,628
33,300 EQT Midstream Partners, L.P.................................................. 1,022,976
131,223 Holly Energy Partners, L.P. (a).............................................. 8,811,624
128,600 Magellan Midstream Partners, L.P. (a)........................................ 5,720,128
88,500 MPLX, L.P.................................................................... 2,554,110
173,239 Natural Resource Partners, L.P. (a).......................................... 3,227,443
286,000 NuStar Energy, L.P. (a)...................................................... 13,110,240
29,600 NuStar GP Holdings, LLC...................................................... 828,208
106,000 ONEOK Partners, L.P. (a)..................................................... 6,174,500
188,886 Plains All American Pipeline, L.P. (a)....................................... 8,798,310
117,700 Spectra Energy Partners, L.P. (a)............................................ 3,506,283
80,709 Sunoco Logistics Partners, L.P. (a).......................................... 4,101,631
303,095 TC Pipelines, L.P. (a)....................................................... 12,636,031
304,828 Teekay LNG Partners, L.P. (a)................................................ 11,534,691
246,570 TransMontaigne Partners, L.P. (a)............................................ 8,563,376
66,300 Williams Partners, L.P. (a).................................................. 3,375,333
--------------
116,977,664
--------------

TOTAL MASTER LIMITED PARTNERSHIPS............................................ 132,186,381
(Cost $118,647,864) --------------

TOTAL INVESTMENTS - 131.5%................................................... 524,981,099
(Cost $485,372,465) (c) --------------

NUMBER OF
CONTRACTS DESCRIPTION VALUE
------------ ----------------------------------------------------------------------------- --------------
CALL OPTIONS WRITTEN - (0.2%)

Centerpoint Energy, Inc. Calls
700 @ $20.00 due February 2013................................................... (28,000)
2,510 @ 22.50 due February 2013................................................... (12,550)
400 @ 22.50 due May 2013........................................................ (4,000)
--------------
(44,550)
--------------
Dominion Resources, Inc. Calls
1,069 @ 55.00 due January 2013.................................................... (3,207)
1,800 @ 57.50 due January 2013.................................................... (5,400)
500 @ 55.00 due April 2013...................................................... (13,000)
--------------
(21,607)
--------------
Duke Energy Corp. Calls
1,291 @ 67.50 due January 2013 .................................................. (19,365)
600 @ 70.00 due January 2013 .................................................. (1,800)
500 @ 70.00 due April 2013 .................................................... (10,000)
--------------
(31,165)
--------------
Enbridge, Inc. Calls
1,000 @ 40.00 due December 2012 ................................................. (70,000)

See Notes to Financial Statements Page 7

FIRST TRUST ENERGY INFRASTRUCTURE FUND
PORTFOLIO OF INVESTMENTS - (CONTINUED)
NOVEMBER 30, 2012

NUMBER OF
CONTRACTS DESCRIPTION VALUE
------------ ----------------------------------------------------------------------------- --------------

CALL OPTIONS WRITTEN - (CONTINUED)

Enbridge, Inc. Calls (Continued)
149 @ $45.00 due April 2013 ............................................. $ (2,235)
700 @ 45.00 due July 2013 .............................................. (28,000)
--------------
(100,235)
--------------
Exelon Corp. Call
1,000 @ 32.00 due January 2013 ........................................... (16,000)
--------------
Kinder Morgan, Inc. Calls
500 @ 37.50 due December 2012 .......................................... (1,000)
400 @ 35.00 due December 2012 .......................................... (10,800)
1,100 @ 37.50 due January 2013 ........................................... (14,300)
1,264 @ 40.00 due March 2013 ............................................. (22,120)
--------------
(48,220)
--------------
NextEra Energy, Inc. Calls
500 @ 72.50 due December 2012 .......................................... (1,500)
1,240 @ 70.00 due January 2013 ........................................... (74,400)
385 @ 72.50 due January 2013 ........................................... (3,850)
--------------
(79,750)
--------------
Northeast Utilities Call
900 @ 40.00 due April 2013 .............................................. (69,750)
--------------
Questar Corp. Calls
547 @ 22.00 due January 2013 ............................................ (2,735)
1,053 @ 21.00 due January 2013 ............................................ (5,265)
457 @ 21.00 due April 2013 .............................................. (11,425)
750 @ 22.00 due April 2013 .............................................. (7,500)
--------------
(26,925)
--------------
Sempra Energy Call
750 @ 67.50 due January 2013 ............................................ (120,000)
--------------
Southern Co. Calls
1,000 @ 44.00 due December 2012 ........................................... (30,000)
1,379 @ 47.00 due January 2013 ............................................ (5,516)
800 @ 50.00 due January 2013 ............................................ (800)
400 @ 44.00 due February 2013 ........................................... (29,000)
--------------
(65,316)
--------------
Spectra Energy Corp. Calls
1,400 @ 31.00 due December 2012 ........................................... (7,000)
1,190 @ 29.00 due January 2013 ............................................ (26,775)
1,000 @ 29.00 due March 2013 .............................................. (45,000)
1,000 @ 31.00 due March 2013 .............................................. (10,000)
--------------
(88,775)
--------------
TransCanada Corp. Call
1,000 @ 50.00 due May 2013 ................................................ (40,000)
--------------

Page 8 See Notes to Financial Statements

FIRST TRUST ENERGY INFRASTRUCTURE FUND
PORTFOLIO OF INVESTMENTS - (CONTINUED)
NOVEMBER 30, 2012

NUMBER OF
CONTRACTS DESCRIPTION VALUE
------------ ----------------------------------------------------------------------------- --------------
CALL OPTIONS WRITTEN - (CONTINUED)

UGI Corp. Call
1,000 @ $35.00 due April 2013 ...................................................... $ (35,000)
--------------
Williams Cos., Inc. Calls
2,000 @ 35.00 due January 2013 ................................................... (98,000)
1,000 @ 39.00 due January 2013 ................................................... (9,000)
--------------
(107,000)
--------------

TOTAL CALL OPTIONS WRITTEN ................................................... (894,293)
(Premiums received $1,576,846) --------------

OUTSTANDING LOAN - (35.5%) ................................................... (141,900,000)

NET OTHER ASSETS AND LIABILITIES - 4.2% ...................................... 16,904,929
--------------
NET ASSETS - 100.0% .......................................................... $ 399,091,735
==============

------------------------------
(a) All or a portion of this security serves as collateral on the
outstanding loan.
(b) Non-income producing security which pays in-kind distributions.
(c) Aggregate cost for federal income tax purposes is $484,513,943. As
of November 30, 2012, the aggregate gross unrealized appreciation
for all securities in which there was an excess of value over tax
cost was $49,406,843 and the aggregate gross unrealized
depreciation for all securities in which there was an excess of
tax cost over value was $8,939,687.

ADR American Depositary Receipt
CAD Canadian Dollar - Security is denominated in Canadian Dollars and
is translated into U.S. Dollars based upon the current exchange
rate.

VALUATION INPUTS
A summary of the inputs used to value the Fund's investments as of November 30,
2012 is as follows (see Note 2A - Portfolio Valuation in the Notes to Financial
Statements):

ASSETS TABLE
LEVEL 2 LEVEL 3
TOTAL LEVEL 1 SIGNIFICANT SIGNIFICANT
VALUE AT QUOTED OBSERVABLE UNOBSERVABLE
11/30/2012 PRICES INPUTS INPUTS
------------ ------------ ------------ ------------

Common Stocks*................................ $392,794,718 $392,794,718 $ -- $ --
Master Limited Partnerships*.................. 132,186,381 132,186,381 -- --
------------ ------------ ------------ ------------
TOTAL INVESTMENTS............................. $524,981,099 $524,981,099 $ -- $ --
============ ============ ============ ============

LIABILITIES TABLE
LEVEL 2 LEVEL 3
TOTAL LEVEL 1 SIGNIFICANT SIGNIFICANT
VALUE AT QUOTED OBSERVABLE UNOBSERVABLE
11/30/2012 PRICES INPUTS INPUTS
------------ ------------ ------------ ------------

Call Options Written.......................... $ (894,293) $ (894,293) $ -- $ --
------------ ------------ ------------ ------------

* See Portfolio of Investments for industry breakout.

All transfers in and out of the Levels during the period are assumed to be
transferred on the last day of the period at their current value. As of November
30, 2012, the Fund transferred common stock valued at $25,390,178 from Level 2
to Level 1 of the fair value hierarchy. The common stock that transferred from
Level 2 to Level 1 did so as a result of the security no longer being
restricted. This common stock was previously fair valued in accordance with
procedures adopted by the Fund's Board of Trustees and the provisions of the
Investment Company Act of 1940, as amended.

See Notes to Financial Statements Page 9

FIRST TRUST ENERGY INFRASTRUCTURE FUND
STATEMENT OF ASSETS AND LIABILITIES
NOVEMBER 30, 2012

ASSETS:

Investments, at value
(Cost $485,372,465) ......................................................................... $ 524,981,099
Cash .......................................................................................... 13,999,594
Prepaid expenses .............................................................................. 15,567
Receivables:
Dividends.................................................................................. 2,089,168
Investment securities sold................................................................. 1,876,498
--------------
Total Assets............................................................................. 542,961,926
--------------
LIABILITIES:
Outstanding loan .............................................................................. 141,900,000
Options written, at value (Premiums received $1,576,846) ...................................... 894,293
Payables:
Investment advisory fees................................................................... 437,055
Investment securities purchased............................................................ 388,163
Interest and fees on loan.................................................................. 102,448
Audit and tax fees......................................................................... 50,300
Administrative fees........................................................................ 35,224
Printing fees.............................................................................. 24,985
Legal fees................................................................................. 12,456
Custodian fees............................................................................. 7,385
Transfer agent fees........................................................................ 6,449
Trustees' fees and expenses................................................................ 5,929
Financial reporting fees................................................................... 771
Other liabilities ............................................................................. 4,733
--------------
Total Liabilities........................................................................ 143,870,191
--------------
NET ASSETS................................................................................. $ 399,091,735
==============
NET ASSETS CONSIST OF:
Paid-in capital ............................................................................... $ 334,446,324
Par value ..................................................................................... 175,502
Accumulated net investment income (loss) ...................................................... 1,024,721
Accumulated net realized gain (loss) on investments, written options and foreign
currency transactions ........................................................................ 23,153,303
Net unrealized appreciation (depreciation) on investments, written options and
foreign currency translation ................................................................. 40,291,885
--------------
NET ASSETS..................................................................................... $ 399,091,735
==============
NET ASSET VALUE, per Common Share (par value $0.01 per Common Share) .......................... $ 22.74
==============
Number of Common Shares outstanding (unlimited number of Common Shares has been authorized).... 17,550,236
==============

Page 10 See Notes to Financial Statements

FIRST TRUST ENERGY INFRASTRUCTURE FUND
STATEMENT OF OPERATIONS
FOR THE YEAR ENDED NOVEMBER 30, 2012

INVESTMENT INCOME:

Dividends (net of foreign withholding tax of $576,589)......................................... $ 11,974,827
Interest....................................................................................... 4,691
--------------
Total investment income..................................................................... 11,979,518
--------------
EXPENSES:
Investment advisory fees....................................................................... 5,206,684
Interest and fees on loan...................................................................... 1,170,682
Administrative fees............................................................................ 420,501
Legal fees..................................................................................... 92,756
Printing fees.................................................................................. 85,897
Audit and tax fees............................................................................. 50,764
Trustees' fees and expenses.................................................................... 36,125
Transfer agent fees............................................................................ 34,871
Custodian fees................................................................................. 31,215
Financial reporting fees....................................................................... 9,250
Other.......................................................................................... 54,925
--------------
Total expenses.............................................................................. 7,193,670
--------------
NET INVESTMENT INCOME (LOSS)................................................................... 4,785,848
--------------
NET REALIZED AND UNREALIZED GAIN (LOSS):
Net realized gain (loss) on:
Investments................................................................................. 34,463,267
Written options (a)......................................................................... 2,239,787
Foreign currency transactions............................................................... (81,244)
--------------
Net realized gain (loss)....................................................................... 36,621,810
--------------
Net increase from payment from the sub-advisor................................................. 104
--------------
Net change in unrealized appreciation (depreciation) on:
Investments................................................................................. 4,236,303
Written options (a)......................................................................... 963,083
Foreign currency translation................................................................ (1,000)
--------------
Net change in unrealized appreciation (depreciation)........................................... 5,198,386
--------------
NET REALIZED AND UNREALIZED GAIN (LOSS)........................................................ 41,820,300
--------------
NET INCREASE (DECREASE) IN NET ASSETS RESULTING FROM OPERATIONS................................ $ 46,606,148
==============

(a) Primary risk exposure is equity option contracts.

See Notes to Financial Statements Page 11

FIRST TRUST ENERGY INFRASTRUCTURE FUND
STATEMENT OF CHANGES IN NET ASSETS

YEAR PERIOD
ENDED ENDED
11/30/2012 11/30/2011 (a)
-------------- --------------

OPERATIONS:
Net investment income (loss)....................................................... $ 4,785,848 $ 912,374
Net realized gain (loss)........................................................... 36,621,810 4,706,818
Net increase from payment from the Sub-Advisor..................................... 104 --
Net change in unrealized appreciation (depreciation)............................... 5,198,386 35,093,499
------------ ------------
Net increase (decrease) in net assets resulting from operations.................... 46,606,148 40,712,691
------------ ------------
DISTRIBUTIONS TO SHAREHOLDERS FROM:
Net investment income.............................................................. (5,424,795) --
Net realized gain.................................................................. (17,425,612) --
Return of capital.................................................................. -- --
------------ ------------
Total distributions to shareholders................................................ (22,850,407) --
------------ ------------
CAPITAL TRANSACTIONS:
Proceeds from Common Shares sold .................................................. -- 335,209,508 (b)
Proceeds from Common Shares reinvested............................................. -- --
Offering costs..................................................................... 103,795 (690,000)
------------ ------------
Net increase (decrease) in net assets resulting from capital transactions.......... 103,795 334,519,508
------------ ------------
Total increase (decrease) in net assets............................................ 23,859,536 375,232,199

NET ASSETS:
Beginning of period................................................................ 375,232,199 --
------------ ------------
End of period...................................................................... $399,091,735 $375,232,199
============ ============
Accumulated net investment income (loss) at end of period.......................... $ 1,024,721 $ 509,363
============ ============
CAPITAL TRANSACTIONS WERE AS FOLLOWS:
Common Shares at beginning of period............................................... 17,550,236 --
Common Shares sold................................................................. -- 17,550,236 (b)
Common Shares issued as reinvestment under the Dividend Reinvestment Plan.......... -- --
------------ ------------
Common Shares at end of period..................................................... 17,550,236 17,550,236
============ ============

-------------------------------------------------------------
(a) The Fund was seeded on August 18, 2011 and commenced operations on
September 27, 2011.

(b) Includes 295,000 shares sold from the over allotment option of the initial
public offering. The shares were sold on November 10, 2011, the trade date,
at the initial offering price of $19.10, which differed from the closing
common share price of $20.01 and the closing NAV per share of $20.85 on
that date.

Page 12 See Notes to Financial Statements

FIRST TRUST ENERGY INFRASTRUCTURE FUND
STATEMENT OF CASH FLOWS
FOR THE YEAR ENDED NOVEMBER 30, 2012

CASH FLOWS FROM OPERATING ACTIVITIES:

Net increase (decrease) in net assets resulting from operations....... $ 46,606,148
Adjustments to reconcile net increase (decrease) in net assets
resulting from operations to net cash used in operating activities:
Purchases of investments........................................... (282,645,366)
Sales of investments............................................... 233,794,181
Proceeds from written options...................................... 4,984,417
Amount paid to close written options............................... (1,247,404)
Return of capital received from investment in MLPs................. 8,209,784
Net realized gain/loss on investments and options.................. (36,703,054)
Net change in unrealized appreciation/depreciation on investments
and options...................................................... (5,199,386)
Net increase from payment from Sub-Advisor......................... (104)

CHANGES IN ASSETS AND LIABILITIES:
Decrease in interest receivable.................................... 6,754
Increase in dividends receivable (a)............................... (822,384)
Increase in prepaid expenses....................................... (9,468)
Increase in interest and fees on loan payable...................... 32,428
Increase in investment advisory fees payable....................... 74,940
Decrease in audit and tax fees payable............................. (200)
Increase in legal fees payable..................................... 6,388
Increase in printing fees payable.................................. 865
Increase in administrative fees payable............................ 5,611
Decrease in custodian fees payable................................. (21,975)
Decrease in offering cost payable.................................. (525,504)
Increase in transfer agent fees payable............................ 4,282
Decrease in Trustees' fees and expenses payable.................... (501)
Decrease in financial reporting fees payable....................... (719)
Increase in other liabilities payable.............................. 3,889
--------------
CASH USED IN OPERATING ACTIVITIES..................................... $ (33,446,378)
---------------

CASH FLOWS FROM FINANCING ACTIVITIES:
Distributions to Common Shareholders from net realized gain........ (5,109,829)
Distributions to Common Shareholders from net investment income.... (17,740,578)
Offering costs..................................................... 103,795
Issuances of loan.................................................. 39,900,000
--------------
CASH FLOWS PROVIDED BY FINANCING ACTIVITIES........................... 17,153,388
---------------
Decrease in cash...................................................... (16,292,990)
Cash at beginning of period........................................... 30,292,584
_______________
CASH AT END OF PERIOD................................................. $ 13,999,594
===============
Supplemental disclosure of cash flow information:
Cash paid during the period for interest and fees..................... $ 1,138,254
===============

-------------------------------------------------------------
(a) Includes net change in unrealized appreciation (depreciation) on
foreign currency of ($1,000).

See Notes to Financial Statements Page 13

FIRST TRUST ENERGY INFRASTRUCTURE FUND
FINANCIAL HIGHLIGHTS
FOR A COMMON SHARE OUTSTANDING THROUGHOUT EACH PERIOD

YEAR PERIOD
ENDED ENDED
11/30/2012 11/30/2011 (a)
------------- -----------------

Net asset value, beginning of period $ 21.38 $ 19.10 (b)
----------- -----------
INCOME FROM INVESTMENT OPERATIONS
Net investment income (loss) 0.27 0.05
Net realized and unrealized gain (loss) 2.38 2.30
----------- -----------
Total from investment operations 2.65 2.35
----------- -----------
Common Shares offering costs charged to paid-in capital 0.01 (0.04)
----------- -----------
Capital reduction from issuance of Common Shares related to over allotment -- (0.03)
----------- -----------
DISTRIBUTIONS PAID TO SHAREHOLDERS FROM:
Net investment income (1.01) --
Net realized gain (0.29) --
Return of capital -- --
----------- -----------
Total from distributions (1.30) --
----------- -----------
Net asset value, end of period $ 22.74 $ 21.38
=========== ===========
Market value, end of period $ 21.34 $ 19.82
=========== ===========
TOTAL RETURN BASED ON NET ASSET VALUE (c) 13.08% (d) 11.94%
=========== ===========
TOTAL RETURN BASED ON MARKET VALUE (c) 14.47% (0.90)%
=========== ===========

--------------------

RATIOS TO AVERAGE NET ASSETS/SUPPLEMENTAL DATA:
Net assets, end of period (in 000's) $ 399,092 $ 375,232
Ratio of total expenses to average net assets 1.82% 1.66% (e)
Ratio of total expenses to average net assets excluding interest expense and
fees on loan 1.52% 1.48% (e)
Ratio of net investment income (loss) to average net assets 1.21% 1.49% (e)
Portfolio turnover rate 46% 8%
INDEBTEDNESS:
Total loan outstanding (in 000's) $ 141,900 $ 102,000
Asset coverage per $1,000 of indebtedness (f) $ 3,812 $ 4,679

--------------------------
(a) Initial seed date of August 18, 2011. The Fund commenced
operations on September 27, 2011.
(b) Net of sales load of $0.90 per Common Share on initial offering.
(c) Total return is based on the combination of reinvested dividend,
capital gain and return of capital distributions, if any, at
prices obtained by the Dividend Reinvestment Plan, and changes in
net asset value per share for net asset value returns and changes
in Common Share price for market value returns. Total returns do
not reflect sales load and are not annualized for periods less
than one year. Past performance is not indicative of future
results.
(d) The Fund received a reimbursement from the Sub-Advisor in the
amount of $104 in connection with a trade error. The reimbursement
from the Sub-Advisor represents less than $0.01 per share and had
no effect on the Fund's total return.
(e) Annualized.
(f) Calculated by taking the Fund's total assets less the Fund's total
liabilities (not including the loan outstanding) and dividing by
the outstanding loan balance in 000's.

Page 14 See Notes to Financial Statements

--------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS
--------------------------------------------------------------------------------

FIRST TRUST ENERGY INFRASTRUCTURE FUND
NOVEMBER 30, 2012

1. FUND DESCRIPTION

First Trust Energy Infrastructure Fund (the "Fund") is a non-diversified,
closed-end management investment company organized as a Massachusetts business
trust on February 22, 2011 and is registered with the Securities and Exchange
Commission ("SEC") under the Investment Company Act of 1940, as amended (the
"1940 Act"). The Fund trades under the ticker symbol FIF on the New York Stock
Exchange ("NYSE").

The Fund's investment objective is to seek a high level of total return with an
emphasis on current distributions paid to shareholders. The Fund seeks to
achieve its objective by investing primarily in securities of companies engaged
in the energy infrastructure sector. Energy infrastructure companies principally
include publicly-traded master limited partnerships and limited liability
companies taxed as partnerships ("MLPs"), MLP affiliates, Canadian income trusts
and their successor companies (collectively, "Canadian Income Equities"),
pipeline companies, utilities, and other companies that derive at least 50% of
their revenues from operating or providing services in support of infrastructure
assets such as pipelines, power transmission and petroleum and natural gas
storage in the petroleum, natural gas and power generation industries
(collectively, "Energy Infrastructure Companies"). For purposes of the Fund's
investment objective, total return includes capital appreciation of, and all
distributions received from, securities in which the Fund will invest, taking
into account the varying tax characteristics of such securities. There can be no
assurance that the Fund will achieve its investment objective. The Fund may not
be appropriate for all investors.

2. SIGNIFICANT ACCOUNTING POLICIES

The following is a summary of significant accounting policies consistently
followed by the Fund in the preparation of its financial statements. The
preparation of financial statements in accordance with accounting principles
generally accepted in the United States of America ("U.S. GAAP") requires
management to make estimates and assumptions that affect the reported amounts
and disclosures in the financial statements. Actual results could differ from
those estimates.

A. PORTFOLIO VALUATION:

The net asset value ("NAV") of the Common Shares of the Fund is determined daily
as of the close of regular trading on the NYSE, normally 4:00 p.m. Eastern time,
on each day the NYSE is open for trading. If the NYSE closes early on a
valuation day, the NAV is determined as of that time. The NAV per Common Share
is calculated by dividing the value of all assets of the Fund (including accrued
interest and dividends), less all liabilities (including accrued expenses,
dividends declared but unpaid and any borrowings of the Fund) by the total
number of Common Shares outstanding.

The Fund's investments are valued daily in accordance with valuation procedures
adopted by the Fund's Board of Trustees, and in accordance with provisions of
the 1940 Act. The Fund's securities, will be valued as follows:

Common stocks, MLPs and other equity securities listed on any national or
foreign exchange (excluding the NASDAQ(R) Stock Market, LLC ("NASDAQ") and
the London Stock Exchange Alternative Investment Market ("AIM")) are valued
at the last sale price on the exchange on which they are principally traded
or, for NASDAQ and AIM securities, the official closing price. Securities
traded on more than one securities exchange are valued at the last sale
price or official closing price, as applicable, at the close of the
securities exchange representing the principal market for such securities.

Exchange-traded options and futures contracts are valued at the closing
price in the market where such contracts are principally traded. If no
closing price is available, exchange-traded options and futures contracts
are valued at the mean between the most recent bid and asked prices.
Over-the-counter options and futures contracts are valued at their closing
bid prices.

Short-term investments that mature in less than 60 days when purchased are
valued at amortized cost.

All market quotations used in valuing the Fund's securities will be obtained
from a third party pricing service. If no quotation is received from a pricing
service, attempts will be made to obtain one or more broker quotes for the
security. In the event the pricing service does not provide a valuation, broker
quotations are not readily available, or the valuations received are deemed
unreliable, the Fund's Board of Trustees has designated First Trust Advisors
L.P. ("First Trust") to use a fair value method to value the Fund's securities.
Additionally, if events occur after the close of the principal markets for
certain securities (e.g., domestic debt and foreign securities) that could
materially affect the Fund's NAV, First Trust will use a fair value method to
value the Fund's securities. The use of fair value pricing is governed by
valuation procedures adopted by the Fund's Board of Trustees, and in accordance
with the provisions of the 1940 Act. As a general principle, the fair value of a
security is the amount which the Fund might reasonably expect to receive for the
security upon its current sale. In light of the judgment involved in fair
valuations, there can be no assurance that a fair value assigned to a particular
security will be the amount which the Fund might be able to receive upon its
current sale. Fair valuation of a security will be based on the consideration of
all available information, including, but not limited to the following:

1) the type of security;
2) the size of the holding;
3) the initial cost of the security;
4) transactions in comparable securities;
5) price quotes from dealers and/or pricing services;
6) relationships among various securities;
7) information obtained by contacting the issuer, analysts, or
the appropriate stock exchange;

Page 15

--------------------------------------------------------------------------------
NOTES TO FINANCIAL STATEMENTS - (CONTINUED)
--------------------------------------------------------------------------------

FIRST TRUST ENERGY INFRASTRUCTURE FUND
NOVEMBER 30, 2012

8) an analysis of the issuer's financial statements; and
9) the existence of merger proposals or tender offers that might
affect the value of the security.

If the securities in question are foreign securities, the following additional
information may be considered:

1) the value of similar foreign securities traded on other
foreign markets;
2) ADR trading of similar securities;
3) closed-end fund trading of similar securities;
4) foreign currency exchange activity;
5) the trading prices of financial products that are tied to
baskets of foreign securities;
6) factors relating to the event that precipitated the pricing
problem;
7) whether the event is likely to recur; and
8) whether the effects of the event are isolated or whether they affect
entire markets, countries or regions.

The Fund is subject to fair value accounting standards that define fair value,
establish the framework for measuring fair value and provide a three-level
hierarchy for fair valuation based upon the inputs to the valuation as of the
measurement date. The three levels of the fair value hierarchy are as follows:

o Level 1 - Level 1 inputs are quoted prices in active
markets for identical investments. An active market is a
market in which transactions for the investment occur with
sufficient frequency and volume to provide pricing
information on an ongoing basis.
o Level 2 - Level 2 inputs are observable inputs, either
directly or indirectly, and include the following:
- Quoted prices for similar investments in active
markets.
- Quoted prices for identical or similar investments in
markets that are non-active. A non-active market is a
market where there are few transactions for the
investment, the prices are not current, or price
quotations vary substantially either over time or
among market makers, or in which little information is
released publicly.
- Inputs other than quoted prices that are observable
for the investment (for example, interest rates and
yield curves observable at commonly quoted intervals,
volatilities, prepayment speeds, loss severities,
credit risks, and default rates).
- Inputs that are derived principally from or
corroborated by observable market data by correlation
or other means.
o Level 3 - Level 3 inputs are unobservable inputs.
Unobservable inputs may reflect the reporting entity's own
assumptions about the assumptions that market participants
would use in pricing the investment.

The inputs or methodology used for valuing investments are not necessarily an
indication of the risk associated with investing in those investments. A summary
of the inputs used to value the Fund's investments as of November 30, 2012, is
included with the Fund's Portfolio of Investments.

B. OPTION CONTRACTS:

The Fund is subject to equity price risk in the normal course of pursuing its
investment objective and may enter into options written to hedge against changes
in the value of equities. Also, by writing (selling) options, the Fund seeks to
generate additional income, in the form of premiums received for writing
(selling) the options. The Fund may write (sell) covered call or put options
("options") on all or a portion of the common stock of energy companies held in
the Fund's portfolio as determined to be appropriate by Energy Income Partners,
LLC ("EIP" or the "Sub-Advisor"). The number of options the Fund can write
(sell) is limited by the amount of common stock of energy companies the Fund
holds in its portfolio. The Fund will not write (sell) "naked" or uncovered
options. When the Fund writes (sells) an option, an amount equal to the premium
received by the Fund is included in "Options written, at value" on the Fund's
Statement of Assets and Liabilities. Options are marked-to-market daily and
their value will be affected by changes in the value and dividend rates of the
underlying equity securities, changes in interest rates, changes in the actual
or perceived volatility of the securities markets and the underlying equity
securities and the remaining time to the options' expiration. The value of
options may also be adversely affected if the market for the options becomes
less liquid or trading volume diminishes.

Options the Fund writes (sells) will either be exercised, expire or be cancelled
pursuant to a closing transaction. If the price of the underlying equity
security exceeds the option's exercise price, it is likely that the option
holder will exercise the option. If an option written (sold) by the Fund is
exercised, the Fund would be obligated to deliver the underlying equity security
to the option holder upon payment of the strike price. In this case, the option
premium received by the Fund will be added to the amount realized on the sale of
the underlying security for purposes of determining gain or loss. If the price
of the underlying equity security is less than the option's strike price, the
option will likely expire without being exercised. The option premium received
by the Fund will, in this case, be treated as short-term capital gain on the
expiration date of the option. The Fund may also elect to close out its position
in an option prior to its expiration by purchasing an option of the same series
as the option written (sold) by the Fund. Gain or loss on options is presented
separately as "Net realized gain (loss) on written options" on the Statement of
Operations.

The options that the Fund writes (sells) give the option holder the right, but
not the obligation, to purchase a security from the Fund at the strike price on
or prior to the option's expiration date. The ability to successfully implement
the writing (selling) of covered call options depends on the ability of the
Sub-Advisor to predict pertinent market movements, which cannot be assured.
Thus, the use of options may require the Fund to sell portfolio securities at
inopportune times or for prices other than current market value, which may limit
the amount of appreciation the Fund can realize on an investment, or may cause
the Fund to hold a security that it might otherwise sell. As the writer (seller)
of a covered option, the Fund foregoes, during the option's life, the
opportunity to profit from increases in the market value of the security

Page 16

FIRST TRUST ENERGY INFRASTRUCTURE FUND
NOVEMBER 30, 2012

covering the option above the sum of the premium and the strike price of the
option, but has retained the risk of loss should the price of the underlying
security decline. The writer (seller) of an option has no control over the time
when it may be required to fulfill its obligation as a writer (seller) of the
option. Once an option writer (seller) has received an exercise notice, it
cannot effect a closing purchase transaction in order to terminate its
obligation under the option and must deliver the underlying security to the
option holder at the exercise price.

Over-the-counter ("OTC") options have the risk of the potential inability of
counterparties to meet the terms of their contracts. The Fund's maximum equity
price risk for purchased options is limited to the premium initially paid. In
addition, certain risks may arise upon entering into option contracts including
the risk that an illiquid secondary market will limit the Fund's ability to
close out an option contract prior to the expiration date and that a change in
the value of the option contract may not correlate exactly with changes in the
value of the securities hedged.

C. SECURITIES TRANSACTIONS AND INVESTMENT INCOME:

Securities transactions are recorded as of the trade date. Realized gains and
losses from securities transactions are recorded on the identified cost basis.
Dividend income is recorded on the ex-dividend date. The Fund will rely to some
extent on information provided by the MLPs, which is not necessarily timely, to
estimate taxable income allocable to the MLP units held in the Fund's portfolio.

Distributions received from the Fund's investments in MLPs generally are
comprised of return of capital and investment income. The Fund records estimated
return of capital and investment income based on historical information
available from each MLP. These estimates may subsequently be revised based on
information received from the MLPs after their tax reporting periods are
concluded. For the year ended November 30, 2012, distributions of $8,209,784
received from MLPs have been reclassified as return of capital.

D. RESTRICTED SECURITIES:

The Fund may invest up to 15% of its Managed Assets in restricted securities.
Managed Assets means the total asset value of the Fund minus the sum of the
Fund's liabilities other than the principal amount of borrowings. Restricted
securities are securities that may not be offered for public sale without first
being registered under the Securities Act of 1933, as amended (the "1933 Act").
Prior to registration, restricted securities may only be resold in transactions
exempt from registration under Rule 144A under the 1933 Act, normally to
qualified institutional buyers. As of November 30, 2012, the Fund held no
restricted securities.

E. DIVIDENDS AND DISTRIBUTIONS TO SHAREHOLDERS:

The Fund will distribute to holders of its Common Shares monthly dividends of
all or a portion of its net income after the payment of interest in connection
with leverage, if any. Distributions of any long-term capital gains earned by
the Fund are distributed at least annually. Distributions will automatically be
reinvested into additional Common Shares pursuant to the Fund's Dividend
Reinvestment Plan unless cash distributions are elected by the shareholder.

Distributions from income and capital gains are determined in accordance with
income tax regulations, which may differ from U.S. GAAP. Certain capital
accounts in the financial statements are periodically adjusted for permanent
differences in order to reflect their tax character. These permanent differences
are primarily due to the varying treatment of income and gain/loss on portfolio
securities held by the Fund and have no impact on net assets or NAV per share.
Temporary differences, which arise from recognizing certain items of income,
expense and gain/loss in different periods for financial statement and tax
purposes, will reverse at some point in the future. Permanent differences
incurred during the year ended November 30, 2012, primarily as a result of
differing book and tax treatments on the sale of MLP investments, have been
reclassified at year end to reflect an increase in accumulated net investment
income (loss) of $1,154,305 and a decrease in accumulated net realized gain
(loss) on investments of $1,152,828 and a decrease to paid-in capital of $1,477.
Net assets were not affected by these reclassifications.

The tax character of distributions paid during the fiscal year ended November
30, 2012 is as follows:

Distributions paid from:
Ordinary income ......................................... $ 22,850,407

As of November 30, 2012, the components of distributable earnings and net assets
on a tax basis were as follows:

Undistributed ordinary income............................ $ 21,712,858
Undistributed capital gains.............................. 1,606,644
------------
Total undistributed earnings............................. 23,319,502
Accumulated capital and other losses..................... --
Net unrealized appreciation (depreciation)............... 40,467,156
------------
Total accumulated earnings (losses)...................... 63,786,658
Other ................................................... 683,251
Paid-in capital.......................................... 334,621,826
------------
Net assets............................................... $399,091,735
============

Page 17

FIRST TRUST ENERGY INFRASTRUCTURE FUND
NOVEMBER 30, 2012

F. INCOME TAXES:

The Fund intends to continue to qualify as a regulated investment company by
complying with the requirements under Subchapter M of the Internal Revenue Code
of 1986, as amended, which includes distributing substantially all of its net
investment income and net realized gains to shareholders. Accordingly, no
provision has been made for federal or state income taxes. However, due to the
timing and amount of distributions, the Fund may be subject to an excise tax of
4% of the amount by which approximately 98% of the Fund's taxable income exceeds
the distributions from such taxable income for the calendar year.

At November 30, 2012, the Fund had no capital loss carryforward for federal
income tax purposes.

The Fund is subject to accounting standards that establish a minimum threshold
for recognizing, and a system for measuring, the benefits of a tax position
taken or expected to be taken in a tax return. Taxable years ending 2011 and
2012 remain open to federal and state audit. As of November 30, 2012 management
has evaluated the application of these standards to the Fund and has determined
that no provision for income tax is required in the Fund's financial statements
for uncertain tax positions.

G. EXPENSES:

The Fund will pay all expenses directly related to its operations.

H. FOREIGN CURRENCY:

The books and records of the Fund are maintained in U.S. dollars. Foreign
currencies, investments and other assets and liabilities are translated into
U.S. dollars at the exchange rates prevailing at the end of the period.
Purchases and sales of investment securities and items of income and expense are
translated on the respective dates of such transactions. Unrealized gains and
losses on assets and liabilities, other than investments in securities, which
result from changes in foreign currency exchange rates have been included in
"Net change in unrealized appreciation (depreciation) on foreign currency
translation" on the Statement of Operations. Unrealized gains and losses on
investments in securities which result from changes in foreign exchange rates
are included with fluctuations arising from changes in market price and are
shown in "Net change in unrealized appreciation (depreciation) on investments"
on the Statement of Operations. Net realized foreign currency gains and losses
include the effect of changes in exchange rates between trade date and
settlement date on investment security transactions, foreign currency
transactions and interest and dividends received. The portion of foreign
currency gains and losses related to fluctuation in exchange rates between the
initial purchase trade date and subsequent sale trade date is included in "Net
realized gain (loss) on foreign currency transactions" on the Statement of
Operations.

I. ORGANIZATION AND OFFERING COSTS:

Organization costs consisted of costs incurred to establish the Fund and enable
it to legally conduct business. These costs included filing fees, listing fees,
legal services pertaining to the organization of the business and audit fees
relating to the initial registration and auditing the initial statement of
assets and liabilities, among other fees. Offering costs consisted of legal fees
pertaining to the Fund's shares offered for sale, registration fees,
underwriting fees, and printing of the initial prospectus, among other fees.
First Trust paid all organization expenses. The Fund's Common Share offering
costs of $690,000 were recorded as a reduction of the proceeds from the sale of
Common Shares during the period ended November 30, 2011. During the fiscal year
ended November 30, 2012, it was determined that actual offering costs were less
than the estimated offering costs by $103,795. Therefore, paid-in-capital was
increased by that amount in the current fiscal year, as reflected in the
offering costs line item on the Statements of Changes in Net Assets.

J. ACCOUNTING PRONOUNCEMENT:

In May 2011, the Financial Accounting Standards Board ("FASB") issued ASU
2011-04, "Amendments to Achieve Common Fair Value Measurement and Disclosure
Requirements in U.S. GAAP and IFRSs", modifying Topic 820, "Fair Value
Measurements and Disclosures." At the same time, the International Accounting
Standards Board ("IASB") issued International Financial Reporting Standard
("IFRS") 13, "Fair Value Measurement." The objective of the FASB and IASB is
convergence of their guidance on fair value measurements and disclosures.
Specifically, the ASU requires reporting entities to disclose (i) the amounts of
any transfers between Level 1 and Level 2, and the reasons for the transfers,
(ii) for Level 3 fair value measurements, quantitative information about
significant unobservable inputs used, (iii) a description of the valuation
processes used by the reporting entity, and (iv) a narrative description of the
sensitivity of the fair value measurement to changes in unobservable inputs if a
change in those inputs might result in a significantly higher or lower fair
value measurement. The effective date of the ASU is for interim and annual
periods beginning after December 15, 2011, and is therefore not effective for
the current fiscal year. Management is in the process of assessing the impact of
the updated standards on the Fund's financial statements, if any.

3. INVESTMENT ADVISORY FEE, AFFILIATED TRANSACTIONS AND OTHER FEE ARRANGEMENTS

First Trust, the investment advisor to the Fund, is a limited partnership with
one limited partner, Grace Partners of DuPage L.P., and one general partner, The
Charger Corporation. The Charger Corporation is an Illinois corporation
controlled by James A. Bowen, Chief Executive Officer of First Trust. First
Trust is responsible for the ongoing monitoring of the Fund's investment
portfolio, managing the Fund's business affairs and providing certain
administrative services necessary for the management of the Fund. For these
investment management services, First Trust is entitled to a monthly fee
calculated at an annual rate of 1.00% of the Fund's Managed Assets. First Trust
also provides fund reporting services to the Fund for a flat annual fee in the
amount of $9,250.

Page 18

FIRST TRUST ENERGY INFRASTRUCTURE FUND
NOVEMBER 30, 2012

EIP serves as the Fund's sub-advisor and manages the Fund's portfolio subject to
First Trust's supervision. The Sub-Advisor receives a monthly sub-advisory fee
calculated at an annual rate of 0.50% of the Funds Managed Assets that is paid
by First Trust out of its investment advisory fee.

During the year ended November 30, 2012, the Fund received a payment from the
Sub-Advisor of $104 in connection with a trade error.

First Trust Capital Partners, LLC ("FTCP"), an affiliate of First Trust, owns,
through a wholly-owned subsidiary, a 15% ownership interest in each of the
Sub-Advisor and EIP Partners, LLC, an affiliate of the Sub-Advisor. In addition,
as of November 29, 2012, FTCP purchased a preferred interest in the Sub-Advisor.
The preferred interest is non-voting and does not share in the profits or losses
of the Sub-Advisor. The Sub-Advisor may buy back any or all of FTCP's preferred
interest at any time and FTCP may sell back to the Sub-Advisor up to 50% of its
preferred interest on or after July 29, 2014 and any or all of its preferred
interest after November 29, 2015.

BNY Mellon Investment Servicing (US) Inc. serves as the Fund's Administrator,
Fund Accountant and Transfer Agent in accordance with certain fee arrangements.
The Bank of New York Mellon serves as the Fund's Custodian in accordance with
certain fee arrangements.

Effective January 23, 2012, James A. Bowen resigned from his position as the
President and Chief Executive Officer of the Fund. He will continue as a
Trustee, the Chairman of the Board of Trustees and a member of the Executive
Committee. The Board elected Mark R. Bradley to serve as the President and Chief
Executive Officer of the Fund and James M. Dykas to serve as the Treasurer,
Chief Financial Officer and Chief Accounting Officer of the Fund.

Effective January 1, 2012, each Trustee who is not an officer or employee of
First Trust, any sub-advisor or any of their affiliates ("Independent Trustees")
is paid a fixed annual retainer of $125,000 per year and an annual per fund fee
of $4,000 for each closed-end fund or other actively managed fund and $1,000 for
each index fund in the First Trust Fund Complex. The fixed annual retainer is
allocated pro rata among each fund in the First Trust Fund Complex based on net
assets. Prior to January 1, 2012, each Independent Trustee received an annual
retainer of $10,000 per trust for the first 14 trusts of the First Trust Fund
Complex and an annual retainer of $7,500 per trust for each additional trust in
the First Trust Fund Complex. The annual retainer was allocated equally among
each of the trusts.

Additionally, the Lead Independent Trustee is paid $15,000 annually, the
Chairman of the Audit Committee is paid $10,000 annually, and each of the
Chairmen of the Nominating and Governance Committee and the Valuation Committee
is paid $5,000 annually to serve in such capacities, with such compensation
allocated pro rata among each fund in the First Trust Fund Complex based on net
assets. Prior to January 1, 2012, the annual amounts paid were $10,000, $5,000
and $2,500, respectively. Trustees are reimbursed for travel and out-of-pocket
expenses in connection with all meetings. The Lead Independent Trustee and each
Committee chairman will serve two-year terms until December 31, 2013, before
rotating to serve as chairman of another committee or as Lead Independent
Trustee. After December 31, 2013, the Lead Independent Trustee and Committee
Chairmen will rotate every three years. The officers and "Interested" Trustee
receive no compensation from the funds for acting in such capacities.

4. PURCHASES AND SALES OF SECURITIES

Cost of purchases and proceeds from sales of investment securities, excluding
short-term investments, for the year ended November 30, 2012 were $278,838,830
and $235,731,480, respectively.

Written option activity for the Fund was as follows:

NUMBER
OF
WRITTEN OPTIONS CONTRACTS PREMIUMS
-------------------------------------------------------------------------------
Options outstanding at November 30, 2011... 29,526 $ 1,735,315
Options Written............................ 129,778 5,018,919
Options Expired............................ (79,852) (3,136,818)
Options Exercised.......................... (37,604) (1,602,238)
Options Closed............................. (6,614) (438,332)
---------- ------------
Options outstanding at November 30, 2012... 35,234 $ 1,576,846
========== ============

5. BORROWINGS

The Fund has a committed facility agreement with the Bank of Nova Scotia
("Scotia") that has a maximum commitment amount of $145,000,000. Effective
December 10, 2012, the maximum commitment amount increased to $165,000,000. The
borrowing rate under the facility is equal to the 1-month LIBOR plus 65 basis
points. In addition, under the facility, the Fund pays a commitment fee of 0.20%
on the undrawn amount of such facility. The average amount outstanding for the
year ended November 30, 2012 was $124,460,929 with a weighted average interest
rate of 0.89%. As of November 30, 2012, the Fund had outstanding borrowings of
$141,900,000 under this committed facility agreement. The high and low annual
interest rates for the year ended November 30, 2012 were 0.95% and 0.86%,
respectively. The interest rate at November 30, 2012 was 0.86%.

Page 19

FIRST TRUST ENERGY INFRASTRUCTURE FUND
NOVEMBER 30, 2012

6. SWAP TRANSACTIONS

The Fund's Board of Trustees, at a special meeting on March 27, 2012, approved
sub-advisor authority to enter into swap transactions under an ISDA
(International Swaps and Derivatives) Master Agreement with Credit Suisse
International. The swap transactions may be used to hedge against interest rate
risk on leverage. In addition, the Fund already has standing permission to use
derivatives for investment purposes. During the year ended November 30, 2012,
the Fund had no swap transactions.

7. INDEMNIFICATION

The Fund has a variety of indemnification obligations under contracts with its
service providers. The Fund's maximum exposure under these arrangements is
unknown. However, the Fund has not had prior claims or losses pursuant to these
contracts and expects the risk of loss to be remote.

8. RISK CONSIDERATIONS

Risks are inherent in all investing. The following summarizes some, but not all,
of the risks that should be considered for the Fund. For additional information
about the risks associated with investing in the Fund, please see the Fund's
prospectus and statement of additional information, as well as other Fund
regulatory filings.

INVESTMENT AND MARKET RISK: An investment in the Fund's Common Shares is subject
to investment risk, including the possible loss of the entire principal
invested. An investment in Common Shares represents an indirect investment in
the securities owned by the Fund. The value of these securities, like other
market investments, may move up or down, sometimes rapidly and unpredictably.
Common Shares at any point in time may be worth less than the original
investment, even after taking into account the reinvestment of Fund dividends
and distributions. Security prices can fluctuate for several reasons including
the general condition of the securities markets, or when political or economic
events affecting the issuers occur. When the Advisor or Sub-Advisor determines
that it is temporarily unable to follow the Fund's investment strategy or that
it is impractical to do so (such as when a market disruption event has occurred
and trading in the securities is extremely limited or absent), the Fund may take
temporary defensive positions.

INDUSTRY CONCENTRATION RISK: The Fund invests at least 80% of its Managed Assets
in securities issued by Energy Infrastructure Companies. Given this industry
concentration, the Fund is more susceptible to adverse economic or regulatory
occurrences affecting that industry than an investment company that is not
concentrated in a single industry. Energy Infrastructure Company issuers may be
subject to a variety of factors that may adversely affect their business or
operations, including high interest costs in connection with capital
construction programs, high leverage costs associated with environmental and
other regulations, the effects of economic slowdown, surplus capacity, increased
competition from other providers of services, uncertainties concerning the
availability of fuel at reasonable prices, the effects of energy conservation
policies and other factors.

MLP RISK: An investment in MLP units involves risks which differ from an
investment in common stock of a corporation. Holders of MLP units have limited
control and voting rights on matters affecting the partnership. In addition,
there are certain tax risks associated with an investment in MLP units and
conflicts of interest exist between common unit holders and the general partner,
including those arising from incentive distribution payments.

LEVERAGE RISK: The use of leverage results in additional risks and can magnify
the effect of any losses. The funds borrowed pursuant to a leverage borrowing
program constitute a substantial lien and burden by reason of their prior claim
against the income of the Fund and against the net assets of the Fund in
liquidation. If the Fund is not in compliance with certain credit facility
provisions, the Fund may not be permitted to declare dividends or other
distributions.

RESTRICTED SECURITIES RISK: The Fund may invest in unregistered or otherwise
restricted securities. The term "restricted securities" refers to securities
that are unregistered or are held by control persons of the issuer and
securities that are subject to contractual restrictions on their resale. As a
result, restricted securities may be more difficult to value and the Fund may
have difficulty disposing of such assets either in a timely manner or for a
reasonable price. In order to dispose of an unregistered security, the Fund,
where it has contractual rights to do so, may have to cause such security to be
registered. A considerable period may elapse between the time the decision is
made to sell the security and the time the security is registered so that the
Fund could sell it. Contractual restrictions on the resale of securities vary in
length and scope and are generally the result of a negotiation between the
issuer and acquirer of the securities. The Fund would, in either case, bear
market risks during that period.

QUALIFIED DIVIDEND INCOME TAX RISK: There can be no assurance as to what portion
of the distributions paid to the Fund's Common Shareholders will consist of
tax-advantaged qualified dividend income. Certain distributions designated by
the Fund as derived from qualified dividend income will be taxed in the hands of
non-corporate Common Shareholders at the rates applicable to long-term capital
gains, provided certain holding period and other requirements are satisfied by
both the Fund and the Common Shareholders. Additional requirements apply in
determining whether distributions by foreign issuers should be regarded as
qualified dividend income. Certain investment strategies of the Fund will limit
the Fund's ability to meet these requirements and consequently will limit the
amount of qualified dividend income received and distributed by the Fund. A
change in the favorable provisions of the federal tax laws with respect to
qualified dividends may result in a widespread reduction in announced dividends
and may adversely impact the valuation of the shares of dividend-paying
companies.

Page 20

FIRST TRUST ENERGY INFRASTRUCTURE FUND
NOVEMBER 30, 2012

CURRENCY RISK: The value of securities denominated or quoted in foreign
currencies may be adversely affected by fluctuations in the relative currency
exchange rates and by exchange control regulations. The Fund's investment
performance may be negatively affected by a devaluation of a currency in which
the Fund's investments are denominated or quoted. Further, the Fund's investment
performance may be significantly affected, either positively or negatively, by
currency exchange rates because the U.S. dollar value of securities denominated
or quoted in another currency will increase or decrease in response to changes
in the value of such currency in relation to the U.S. dollar. While certain of
the Fund's non-U.S. dollar-denominated securities may be hedged into U.S.
dollars, hedging may not alleviate all currency risks.

NON-U.S. RISK: The Fund may invest a portion of its assets in the equity
securities of issuers domiciled in jurisdictions other than the U.S. Investments
in the securities and instruments of non-U.S. issuers involve certain
considerations and risks not ordinarily associated with investments in
securities and instruments of U.S. issuers. Non-U.S. companies are not generally
subject to uniform accounting, auditing and financial standards and requirements
comparable to those applicable to U.S. companies. Non-U.S. securities exchanges,
brokers and listed companies may be subject to less government supervision and
regulation than exists in the United States. Dividend and interest income may be
subject to withholding and other non-U.S. taxes, which may adversely affect the
net return on such investments. A related risk is that there may be difficulty
in obtaining or enforcing a court judgment abroad.

9. SUBSEQUENT EVENTS

Management has evaluated the impact of all subsequent events on the Fund through
the date the financial statements were issued, and has determined that besides
those subsequent events already disclosed there were the following subsequent
events:

On December 12, 2012, the Fund declared a distribution of long-term capital
gains of $0.095 per share to Common Shareholders of record on December 26, 2012,
payable December 31, 2012.

On December 12, 2012, the Fund declared a distribution of short-term capital
gains of $0.988 per share to Common Shareholders of record on December 26, 2012,
payable December 31, 2012.

On December 12, 2012, the Fund declared a distribution of short-term capital
gains of $0.110 per share to Common Shareholders of record on December 26, 2012,
payable January 15, 2013.

On January 22, 2013, the Fund declared a dividend of $0.110 per share to Common
Shareholders of record on February 5, 2013, payable February 15, 2013.

Page 21

--------------------------------------------------------------------------------
REPORT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM
--------------------------------------------------------------------------------

TO THE BOARD OF TRUSTEES AND SHAREHOLDERS OF FIRST TRUST ENERGY INFRASTRUCTURE
FUND:

We have audited the accompanying statement of assets and liabilities of First
Trust Energy Infrastructure Fund (the "Fund"), including the portfolio of
investments, as of November 30, 2012 and the related statements of operations
and cash flows for the year then ended and the statements of changes in net
assets and the financial highlights for periods presented. These financial
statements and financial highlights are the responsibility of the Fund's
management. Our responsibility is to express an opinion on these financial
statements and financial highlights based on our audits.

We conducted our audits in accordance with the standards of the Public Company
Accounting Oversight Board (United States). Those standards require that we plan
and perform the audits to obtain reasonable assurance about whether the
financial statements and financial highlights are free of material misstatement.
The Fund is not required to have, nor were we engaged to perform, an audit of
its internal control over financial reporting. Our audits included consideration
of internal control over financial reporting as a basis for designing audit
procedures that are appropriate in the circumstances, but not for the purpose of
expressing an opinion on the effectiveness of the Fund's internal control over
financial reporting. Accordingly, we express no such opinion. An audit also
includes examining, on a test basis, evidence supporting the amounts and
disclosures in the financial statements, assessing the accounting principles
used and significant estimates made by management, as well as evaluating the
overall financial statement presentation. Our procedures included confirmation
of securities owned as of November 30, 2012 by correspondence with the Fund's
custodian and brokers; where replies were not received, we performed other
auditing procedures. We believe that our audits provide a reasonable basis for
our opinion.

In our opinion, the financial statements and financial highlights referred to
above present fairly, in all material respects, the financial position of First
Trust Energy Infrastructure Fund, as of November 30, 2012, the results of its
operations and its cash flows for the year then ended, and changes in its net
assets and the financial highlights for the periods presented, in conformity
with accounting principles generally accepted in the United States of America.

/s/ DELOITTE & TOUCHE LLP

Chicago, Illinois
January 28, 2013

Page 22

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ADDITIONAL INFORMATION
--------------------------------------------------------------------------------
FIRST TRUST ENERGY INFRASTRUCTURE FUND
NOVEMBER 30, 2012 (UNAUDITED)

DIVIDEND REINVESTMENT PLAN

If your Common Shares are registered directly with the Fund or if you hold your
Common Shares with a brokerage firm that participates in the Fund's Dividend
Reinvestment Plan (the "Plan"), unless you elect, by written notice to the Fund,
to receive cash distributions, all dividends, including any capital gain
distributions, on your Common Shares will be automatically reinvested by BNY
Mellon Investment Servicing (US) Inc. (the "Plan Agent"), in additional Common
Shares under the Plan. If you elect to receive cash distributions, you will
receive all distributions in cash paid by check mailed directly to you by the
Plan Agent, as the dividend paying agent.

If you decide to participate in the Plan, the number of Common Shares you will
receive will be determined as follows:

(1) If Common Shares are trading at or above net asset value ("NAV") at
the time of valuation, the Fund will issue new shares at a price
equal to the greater of (i) NAV per Common Share on that date or
(ii) 95% of the market price on that date.

(2) If Common Shares are trading below NAV at the time of valuation, the
Plan Agent will receive the dividend or distribution in cash and
will purchase Common Shares in the open market, on the NYSE or
elsewhere, for the participants' accounts. It is possible that the
market price for the Common Shares may increase before the Plan
Agent has completed its purchases. Therefore, the average purchase
price per share paid by the Plan Agent may exceed the market price
at the time of valuation, resulting in the purchase of fewer shares
than if the dividend or distribution had been paid in Common Shares
issued by the Fund. The Plan Agent will use all dividends and
distributions received in cash to purchase Common Shares in the open
market within 30 days of the valuation date except where temporary
curtailment or suspension of purchases is necessary to comply with
federal securities laws. Interest will not be paid on any uninvested
cash payments.

You may elect to opt-out of or withdraw from the Plan at any time by giving
written notice to the Plan Agent, or by telephone at (866) 340-1104, in
accordance with such reasonable requirements as the Plan Agent and the Fund may
agree upon. If you withdraw or the Plan is terminated, you will receive a
certificate for each whole share in your account under the Plan, and you will
receive a cash payment for any fraction of a share in your account. If you wish,
the Plan Agent will sell your shares and send you the proceeds, minus brokerage
commissions.

The Plan Agent maintains all Common Shareholders' accounts in the Plan and gives
written confirmation of all transactions in the accounts, including information
you may need for tax records. Common Shares in your account will be held by the
Plan Agent in non-certificated form. The Plan Agent will forward to each
participant any proxy solicitation material and will vote any shares so held
only in accordance with proxies returned to the Fund. Any proxy you receive will
include all Common Shares you have received under the Plan.

There is no brokerage charge for reinvestment of your dividends or distributions
in Common Shares. However, all participants will pay a pro rata share of
brokerage commissions incurred by the Plan Agent when it makes open market
purchases.

Automatically reinvesting dividends and distributions does not mean that you do
not have to pay income taxes due upon receiving dividends and distributions.
Capital gains and income are realized although cash is not received by you.
Consult your financial advisor for more information.

If you hold your Common Shares with a brokerage firm that does not participate
in the Plan, you will not be able to participate in the Plan and any dividend
reinvestment may be effected on different terms than those described above.

The Fund reserves the right to amend or terminate the Plan if in the judgment of
the Board of Trustees the change is warranted. There is no direct service charge
to participants in the Plan; however, the Fund reserves the right to amend the
Plan to include a service charge payable by the participants. Additional
information about the Plan may be obtained by writing BNY Mellon Investment
Servicing (US) Inc., 301 Bellevue Parkway, Wilmington, Delaware 19809.

--------------------------------------------------------------------------------

PROXY VOTING POLICIES AND PROCEDURES

A description of the policies and procedures that the Fund uses to determine how
to vote proxies and information on how the Fund voted proxies relating to
portfolio investments during the most recent 12-month period ended June 30 is
available (1) without charge, upon request, by calling (800) 988-5891; (2) on
the Fund's website located at http://www.ftportfolios.com; and (3) on the
Securities and Exchange Commission's ("SEC") website located at
http://www.sec.gov.

Page 23

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ADDITIONAL INFORMATION - (CONTINUED)
--------------------------------------------------------------------------------

FIRST TRUST ENERGY INFRASTRUCTURE FUND
NOVEMBER 30, 2012 (UNAUDITED)

PORTFOLIO HOLDINGS

The Fund files its complete schedule of portfolio holdings with the SEC for the
first and third quarters of each fiscal year on Form N-Q. The Fund's Forms N-Q
are available (1) by calling (800) 988-5891; (2) on the Fund's website located
at http://www.ftportfolios.com; (3) on the SEC's website at http://www.sec.gov;
and (4) for review and copying at the SEC's Public Reference Room ("PRR") in
Washington, DC. Information regarding the operation of the PRR may be obtained
by calling (800) SEC-0330.

TAX INFORMATION

Of the ordinary income (including short-term capital gain) distributions made by
the Fund during the year ended November 30, 2012, 14.86% qualified for the
corporate dividends received deduction available to corporate shareholders.

The Fund hereby designates as qualified dividend income 23.52% of the ordinary
income distributions for the year ended November 30, 2012.

NYSE CERTIFICATION INFORMATION

In accordance with Section 303A-12 of the New York Stock Exchange ("NYSE")
Listed Company Manual, the Fund's President has certified to the NYSE that, as
of May 8, 2012, he was not aware of any violation by the Fund of NYSE corporate
governance listing standards. In addition, the Fund's reports to the SEC on
Forms N-CSR, N-CSRS and N-Q contain certifications by the Fund's principal
executive officer and principal financial officer that relate to the Fund's
public disclosure in such reports and are required by Rule 30a-2 under the 1940
Act.

SUBMISSION OF MATTERS TO A VOTE OF SHAREHOLDERS

The Joint Annual Meeting of Shareholders of the Common Shares of First Trust
Energy Income and Growth Fund, First Trust Enhanced Equity Income Fund, First
Trust/Aberdeen Global Opportunity Income Fund, First Trust Mortgage Income Fund,
First Trust Strategic High Income Fund II, First Trust/Aberdeen Emerging
Opportunity Fund, First Trust Specialty Finance and Financial Opportunities
Fund, First Trust Active Dividend Income Fund, First Trust Energy Infrastructure
Fund, Macquarie/First Trust Global Infrastructure/Utilities Dividend & Income
Fund and First Trust High Income Long/Short Fund was held on April 18, 2012 (the
"Annual Meeting"). At the Annual Meeting, Richard E. Erickson and Thomas R.
Kadlec were elected by the Common Shareholders of the First Trust Energy
Infrastructure Fund as Class II Trustees for a three-year term expiring at the
Fund's annual meeting of shareholders in 2015. The number of votes cast in favor
of Mr. Erickson was 16,564,990, the number of votes against was 219,218 and the
number of abstentions was 766,028. The number of votes cast in favor of Mr.
Kadlec was 16,592,516, the number of votes against was 191,692 and the number of
abstentions was 766,028. James A. Bowen, Niel B. Nielson and Robert F. Keith are
the other current and continuing Trustees.

Page 24

--------------------------------------------------------------------------------
BOARD OF TRUSTEES AND OFFICERS
--------------------------------------------------------------------------------

FIRST TRUST ENERGY INFRASTRUCTURE FUND
NOVEMBER 30, 2012 (UNAUDITED)

NUMBER OF
PORTFOLIOS IN
THE FIRST TRUST OTHER
NAME, ADDRESS, TERM OF OFFICE FUND COMPLEX TRUSTEESHIPS OR
DATE OF BIRTH AND AND LENGTH OF PRINCIPAL OCCUPATIONS OVERSEEN BY DIRECTORSHIPS
POSITION WITH THE FUND SERVICE (2) DURING PAST 5 YEARS TRUSTEE HELD BY TRUSTEE

------------------------------------------------------------------------------------------------------------------------------------
INDEPENDENT TRUSTEES
------------------------------------------------------------------------------------------------------------------------------------

Richard E. Erickson, Trustee o Three-Year Term Physician; President, Wheaton Orthopedics; 98 None
c/o First Trust Advisors L.P. Co-Owner and Co-Director (January 1996
120 East Liberty Drive, o Since Fund to May 2007), Sports Med Center for
Suite 400 Inception Fitness; Limited Partner, Gundersen Real
Wheaton, IL 60187 Estate Limited Partnership; Member,
D.O.B.: 04/51 Sportsmed LLC

Thomas R. Kadlec, Trustee o Three-Year Term President (March 2010 to Present), Senior 98 Director of ADM
c/o First Trust Advisors L.P. Vice President and Chief Financial Officer Investor Services,
120 East Liberty Drive, o Since Fund (May 2007 to March 2010), Vice President Inc. and ADM
Suite 400 Inception and Chief Financial Officer (1990 to May Investor Services
Wheaton, IL 60187 2007), ADM Investor Services, Inc. (Futures International
D.O.B.: 11/57 Commission Merchant)

Robert F. Keith, Trustee o Three-Year Term President (2003 to Present), Hibs 98 Director of Trust
c/o First Trust Advisors L.P. Enterprises (Financial and Management Company of
120 East Liberty Drive, o Since Fund Consulting) llinois
Suite 400 Inception
Wheaton, IL 60187
D.O.B.: 11/56

Niel B. Nielson, Trustee o Three-Year Term President and Chief Executive Officer (June 98 Director of
c/o First Trust Advisors L.P. 2012 to Present), Dew Learning LLC Covenant
120 East Liberty Drive, o Since Fund (Educational Products and Services); President Transport Inc.
Suite 400 Inception (June 2002 to June 2012), Covenant College
Wheaton, IL 60187
D.O.B.: 03/54

------------------------------------------------------------------------------------------------------------------------------------
INTERESTED TRUSTEE
------------------------------------------------------------------------------------------------------------------------------------

James A. Bowen(1), Trustee and o Three-Year Term Chief Executive Officer (December 2010 98 None
Chairman of the Board to Present), President (until December
120 East Liberty Drive, o Since Fund 2010), First Trust Advisors L.P. and First
Suite 400 Inception Trust Portfolios L.P.; Chairman of the
Wheaton, IL 60187 Board of Directors, BondWave LLC
D.O.B.: 09/55 (Software Development Company/
Investment Advisor) and Stonebridge
Advisors LLC (Investment Advisor)

-------------
(1) Mr. Bowen is deemed an "interested person" of the Fund due to his position
as Chief Executive Officer of First Trust Advisors L.P., investment advisor
of the Fund.
(2) Currently, Robert F. Keith, as a Class I Trustee, is serving as a trustee
until the Fund's 2014 annual meeting of shareholders. Richard E. Erickson
and Thomas R. Kadlec, as Class II Trustees, are serving as trustees until
the Fund's 2015 annual meeting of shareholders. James A. Bowen and Niel B.
Nielson, as Class III Trustees, are serving as trustees until the Fund's
2013 annual meeting of shareholders.

Page 25

--------------------------------------------------------------------------------
BOARD OF TRUSTEES AND OFFICERS - (CONTINUED)
--------------------------------------------------------------------------------

FIRST TRUST ENERGY INFRASTRUCTURE FUND
NOVEMBER 30, 2012 (UNAUDITED)

NAME, ADDRESS POSITION AND OFFICES TERM OF OFFICE AND PRINCIPAL OCCUPATIONS
AND DATE OF BIRTH WITH FUND LENGTH OF SERVICE DURING PAST 5 YEARS

-----------------------------------------------------------------------------------------------------------------------------------
OFFICERS(3)
-----------------------------------------------------------------------------------------------------------------------------------

Mark R. Bradley President and Chief o Indefinite Term Chief Operating Officer (December 2010 to Present)
120 E. Liberty Drive, Executive Officer and Chief Financial Officer, First Trust Advisors
Suite 400 o President and Chief L.P. and First Trust Portfolios L.P.; Chief
Wheaton, IL 60187 Executive Officer Financial Officer, BondWave LLC (Software Development
D.O.B.: 11/57 Since January 2012 Company/Investment Advisor) and Stonebridge
Advisors LLC (Investment Advisor)
o Treasurer, Chief
Financial Officer and
Chief Accounting
Officer From
Fund Inception
to January 2012

James M. Dykas Treasurer, Chief Financial o Indefinite Term Controller (January 2011 to Present), Senior Vice
120 E. Liberty Drive, Officer and Chief President (April 2007 to January 2011), Vice
Suite 400 Accounting Officer o Treasurer, Chief President (January 2005 to April 2007), First Trust
Wheaton, IL 60187 Financial Officer and Advisors L.P. and First Trust Portfolios L.P.
D.O.B.: 01/66 Chief Accounting
Officer Since
January 2012

o Assistant Treasurer
from Fund Inception to
January 2012

W. Scott Jardine Secretary and Chief Legal o Indefinite Term General Counsel, First Trust Advisors L.P., First
120 E. Liberty Drive, Officer Trust Portfolios L.P. and BondWave LLC
Suite 400 o Since Fund Inception (Software Development Company/Investment
Wheaton, IL 60187 Advisor); Secretary of Stonebridge Advisors LLC
D.O.B.: 05/60 (Investment Advisor)

Daniel J. Lindquist Vice President o Indefinite Term Senior Vice President (September 2005 to
120 E. Liberty Drive, Present), First Trust Advisors L.P. and First Trust
Suite 400 o Since Fund Inception Portfolios L.P. Wheaton, IL 60187
D.O.B.: 02/70

Kristi A. Maher Assistant Secretary and o Indefinite Term Deputy General Counsel (May 2007 to Present),
120 E. Liberty Drive, Chief Compliance Officer First Trust Advisors L.P.and First Trust Portfolios
Suite 400 o Assistant Secretary L.P.
Wheaton, IL 60187 Since Fund Inception
D.O.B.: 12/66
o Chief Compliance
Officer Since Fund
Inception

-------------
(3) Officers of the Fund have an indefinite term. The term "officer"
means the president, vice president, secretary, treasurer, controller
or any other officer who performs a policy making function.

Page 26

--------------------------------------------------------------------------------
PRIVACY POLICY
--------------------------------------------------------------------------------

FIRST TRUST ENERGY INFRASTRUCTURE FUND
NOVEMBER 30, 2012 (UNAUDITED)

First Trust values our relationship with you and considers your privacy an
important priority in maintaining that relationship. We are committed to
protecting the security and confidentiality of your personal information.

SOURCES OF INFORMATION

We collect nonpublic personal information about you from the following sources:

o Information we receive from you and your broker-dealer, investment
advisor or financial representative through interviews, applications,
agreements or other forms;

o Information about your transactions with us, our affiliates or others;

o Information we receive from your inquiries by mail, e-mail or
telephone; and

o Information we collect on our website through the use of "cookies". For
example, we may identify the pages on our website that your browser
requests or visits.

INFORMATION COLLECTED

The type of data we collect may include your name, address, social security
number, age, financial status, assets, income, tax information, retirement and
estate plan information, transaction history, account balance, payment history,
investment objectives, marital status, family relationships and other personal
information.

DISCLOSURE OF INFORMATION

We do not disclose any nonpublic personal information about our customers or
former customers to anyone, except as permitted by law. In addition to using
this information to verify your identity (as required under law), the permitted
uses may also include the disclosure of such information to unaffiliated
companies for the following reasons:

o In order to provide you with products and services and to effect
transactions that you request or authorize, we may disclose your
personal information as described above to unaffiliated financial
service providers and other companies that perform administrative or
other services on our behalf, such as transfer agents, custodians and
trustees, or that assist us in the distribution of investor materials
such as trustees, banks, financial representatives, proxy services,
solicitors and printers.

o We may release information we have about you if you direct us to do so,
if we are compelled by law to do so, or in other legally limited
circumstances (for example to protect your account from fraud).

In addition, in order to alert you to our other financial products and services,
we may share your personal information within First Trust.

PRIVACY ONLINE

We allow third-party companies, including AddThis (a social media sharing
service), to collect certain anonymous information when you visit our website.
These companies may use non-personally identifiable information during your
visits to this and other websites in order to provide advertisements about goods
and services likely to be of greater interest to you. These companies typically
use a cookie, third party web beacon or pixel tags, to collect this information.
To learn more about this behavioral advertising practice, you can visit
www.networkadvertising.org.

CONFIDENTIALITY AND SECURITY

With regard to our internal security procedures, First Trust restricts access to
your nonpublic personal information to those First Trust employees who need to
know that information to provide products or services to you. We maintain
physical, electronic and procedural safeguards to protect your nonpublic
personal information.

POLICY UPDATES AND INQUIRIES

As required by federal law, we will notify you of our privacy policy annually.
We reserve the right to modify this policy at any time, however, if we do change
it, we will tell you promptly. For questions about our policy, or for additional
copies of this notice, please go to www.ftportfolios.com, or contact us at
1-800-621-1675 (First Trust Portfolios) or 1-800-222-6822 (First Trust
Advisors).

Page 27

This Page Left Blank Intentionally.

FIRST TRUST

INVESTMENT ADVISOR
First Trust Advisors L.P.
120 E. Liberty Drive, Suite 400
Wheaton, IL 60187

INVESTMENT SUB-ADVISOR
Energy Income Partners, LLC
49 Riverside Avenue
Westport, CT 06880

ADMINISTRATOR,
FUND ACCOUNTANT &
TRANSFER AGENT
BNY Mellon Investment Servicing (US) Inc.
301 Bellevue Parkway
Wilmington, DE 19809

CUSTODIAN
The Bank of New York Mellon
101 Barclay Street, 20th Floor
New York, NY 10286

INDEPENDENT REGISTERED
PUBLIC ACCOUNTING FIRM
Deloitte & Touche LLP
111 S. Wacker Drive
Chicago, IL 60606

LEGAL COUNSEL
Chapman and Cutler LLP
111 W. Monroe Street
Chicago, IL 60603

[BLANK BACK COVER]

ITEM 2. CODE OF ETHICS.

(a) The registrant, as of the end of the period covered by this report, has
adopted a code of ethics that applies to the registrant's principal
executive officer, principal financial officer, principal accounting
officer or controller, or persons performing similar functions,
regardless of whether these individuals are employed by the registrant or
a third party.

(c) There have been no amendments, during the period covered by this report,
to a provision of the code of ethics that applies to the registrant's
principal executive officer, principal financial officer, principal
accounting officer or controller, or persons performing similar
functions, regardless of whether these individuals are employed by the
registrant or a third party, and that relates to any element of the code
of ethics description.

(d) The registrant has not granted any waivers, including an implicit waiver,
from a provision of the code of ethics that applies to the registrant's
principal executive officer, principal financial officer, principal
accounting officer or controller, or persons performing similar
functions, regardless of whether these individuals are employed by the
registrant or a third party, that relates to one or more of the items set
forth in paragraph (b) of this item's instructions.

ITEM 3. AUDIT COMMITTEE FINANCIAL EXPERT.

As of the end of the period covered by the report, the Registrant's board of
trustees has determined that Thomas R. Kadlec and Robert F. Keith are qualified
to serve as audit committee financial experts serving on its audit committee and
that each of them is "independent," as defined by Item 3 of Form N-CSR.

ITEM 4. PRINCIPAL ACCOUNTANT FEES AND SERVICES.

(a) Audit Fees (Registrant) -- The aggregate fees billed for each of the
last two fiscal years for professional services rendered by the principal
accountant for the audit of the Registrant's annual financial statements or
services that are normally provided by the accountant in connection with
statutory and regulatory filings or engagements for those fiscal years were
$46,000 for the fiscal year beginning from the Registrant's inception on
September 27, 2011 through November 30, 2011 and $44,000 for the fiscal year
ended November 30, 2012.

(b) Audit-Related Fees (Registrant) -- The aggregate fees billed in each
of the last two fiscal years for assurance and related services by the principal
accountant that are reasonably related to the performance of the audit of the
registrant's financial statements and are not reported under paragraph (a)

of this Item were $0 for the fiscal year beginning from the Registrant's
inception on September 27, 2011 through November 30, 2011 and $0 for the fiscal
year ended November 30, 2012.

Audit-Related Fees (Investment Adviser) -- The aggregate fees billed in
each of the last two fiscal years for assurance and related services by the
principal accountant that are reasonably related to the performance of the audit
of the registrant's financial statements and are not reported under paragraph
(a) of this Item were $21,000 for the fiscal year beginning from the
Registrant's inception on September 27, 2011 through November 30, 2011 and $0
for the fiscal year ended November 30, 2012. The Adviser's Audit-Related Fees in
the fiscal year ended November 30, 2011 were for seed audit services, generation
and use of initial consent letters, a comfort letter, and bring-down letters.

(c) Tax Fees (Registrant) -- The aggregate fees billed in each of the last
two fiscal years for professional services rendered by the principal accountant
for tax compliance, tax advice, and tax planning to the registrant were $0 for
the fiscal year beginning from the Registrant's inception on September 27, 2011
through November 30, 2011 and $0 for the fiscal year ended November 30, 2012.

Tax Fees (Investment Adviser) -- The aggregate fees billed in each of the
last two fiscal years for professional services rendered by the principal
accountant for tax compliance, tax advice, and tax planning to the registrant's
adviser were $0 for the fiscal year beginning from the Registrant's inception on
September 27, 2011 through November 30, 2011 and $0 for the fiscal year ended
November 30, 2012.

(d) All Other Fees (Registrant) -- The aggregate fees billed in each of
the last two fiscal years for products and services provided by the principal
accountant to the registrant, other than the services reported in paragraphs (a)
through (c) of this Item were $0 for the fiscal year beginning from the
Registrant's inception on September 27, 2011 through November 30, 2011 and $0
for the fiscal year ended November 30, 2012.

All Other Fees (Investment Adviser) -- The aggregate fees billed in each
of the last two fiscal years for products and services provided by the principal
accountant to the registrant's investment adviser, other than the services
reported in paragraphs (a) through (c) of this Item were $0 for the fiscal year
beginning from the Registrant's inception on September 27, 2011 through November
30, 2011 and $0 for the fiscal year ended November 30, 2012.

(e)(1) Disclose the audit committee's pre-approval policies and procedures
described in paragraph (c)(7) of Rule 2-01 of Regulation S-X.

Pursuant to its charter and its Audit and Non-Audit Services Pre-Approval
Policy, the Audit Committee (the "Committee") is responsible for the
pre-approval of all audit services and permitted non-audit services (including
the fees and terms thereof) to be performed for the Registrant by its
independent auditors. The Chairman of the Committee authorized to give such
pre-approvals on behalf of the Committee up to $25,000 and report any such
pre-approval to the full Committee.

The Committee is also responsible for the pre-approval of the independent
auditor's engagements for non-audit services with the Registrant's adviser (not
including a sub-adviser whose role is primarily portfolio management and is
sub-contracted or overseen by another investment adviser) and any entity
controlling, controlled by or under common control with the investment adviser
that provides

ongoing services to the Registrant, if the engagement relates directly to the
operations and financial reporting of the Registrant, subject to the de minimis
exceptions for non-audit services described in Rule 2-01 of Regulation S-X. If
the independent auditor has provided non-audit services to the Registrant's
adviser (other than any sub-adviser whose role is primarily portfolio management
and is sub-contracted with or overseen by another investment adviser) and any
entity controlling, controlled by or under common control with the investment
adviser that provides ongoing services to the Registrant that were not
pre-approved pursuant to the de minimis exception, the Committee will consider
whether the provision of such non-audit services is compatible with the
auditor's independence.

(e)(2) The percentage of services described in each of paragraphs (b)
through (d) for the Registrant and the Registrant's investment adviser of this
Item that were approved by the audit committee pursuant to the pre-approval
exceptions included in paragraph (c)(7)(i)(c) or paragraph (c)(7)(ii) of Rule
2-01 of Regulation S-X are as follows:

(b) 0%

(d) 0%

(f) The percentage of hours expended on the principal accountant's
engagement to audit the registrant's financial statements for the most recent
fiscal year that were attributed to work performed by persons other than the
principal accountant's full-time, permanent employees was less than fifty
percent.

(g) The aggregate non-audit fees billed by the registrant's accountant for
services rendered to the Registrant, and rendered to the Registrant's investment
adviser (not including any sub-adviser whose role is primarily portfolio
management and is subcontracted with or overseen by another investment adviser),
and any entity controlling, controlled by, or under common control with the
adviser that provides ongoing services to the Registrant for the fiscal year
beginning from the Registrant's inception on September 27, 2011 through November
30, 2011 were $0 for the Registrant and $2,480 for the Registrant's investment
adviser, and for the fiscal year ended November 30, 2012 were $0 for the
registrant and $4,120 for the Registrant's investment adviser.

(h) The Registrant's audit committee of its Board of Trustees has
determined that the provision of non-audit services that were rendered to the
Registrant's investment adviser (not including any sub-adviser whose role is
primarily portfolio management and is subcontracted with or overseen by another
investment adviser), and any entity controlling, controlled by, or under common
control with the investment adviser that provides ongoing services to the
Registrant that were not pre-approved pursuant to paragraph (c)(7)(ii) of Rule
2-01 of Regulation S-X is compatible with maintaining the principal accountant's
independence.

ITEM 5. AUDIT COMMITTEE OF LISTED REGISTRANTS.

The Registrant has a separately designated audit committee consisting of
all the independent trustees of the Registrant. The members of the audit
committee are: Thomas R. Kadlec, Niel B. Nielson, Richard E. Erickson and
Robert F. Keith.

ITEM 6. INVESTMENTS.

(a) Schedule of Investments in securities of unaffiliated issuers as of the
close of the reporting period is included as part of the report to
shareholders filed under Item 1 of this form.

(b) Not applicable.

ITEM 7. DISCLOSURE OF PROXY VOTING POLICIES AND PROCEDURES FOR CLOSED-END
MANAGEMENT INVESTMENT COMPANIES.

PROXY VOTING POLICIES AND PROCEDURES

If an adviser exercises voting authority with respect to client securities,
Advisers Act Rule 206(4)-6 requires the adviser to adopt and implement written
policies and procedures reasonably designed to ensure that client securities are
voted in the best interest of the client. This is consistent with legal
interpretations which hold that an adviser's fiduciary duty includes handling
the voting of proxies on securities held in client accounts over which the
adviser exercises investment or voting discretion, in a manner consistent with
the best interest of the client.

Absent unusual circumstances, EIP exercises voting authority with respect to
securities held in client accounts pursuant to provisions in its advisory
agreements. Accordingly, EIP has adopted these policies and procedures with the
aim of meeting the following requirements of Rule 206(4)-6:

o ensuring that proxies are voted in the best interest of clients;

o addressing material conflicts that may arise between EIP's interests
and those of its clients in the voting of proxies;

o disclosing to clients how they may obtain information on how EIP
voted proxies with respect to the client's securities;

o describing to clients EIP's proxy voting policies and procedures
and, upon request, furnishing a copy of the policies and procedures
to the requesting client.

ENGAGEMENT OF RISKMETRICS GROUP

With the aim of ensuring that proxies are voted in the best interest of
EIP clients, EIP has engaged RiskMetrics Group ("RiskMetrics"), formerly known
as Institutional Shareholder Services, as its independent proxy voting service
to provide EIP with proxy voting recommendations, as well as to handle the
administrative mechanics of proxy voting. EIP has directed RiskMetrics to
utilize its Proxy Voting Guidelines in making recommendations to vote, as those
guidelines may be amended from time to time.

CONFLICTS OF INTEREST IN PROXY VOTING

There may be instances where EIP's interests conflict, or appear to
conflict, with client interests in the voting of proxies. For example, EIP may
provide services to, or have an investor who is a senior member of, a company
whose management is soliciting proxies. There may be a concern that EIP would
vote in favor of management because of its relationship with the company or a
senior officer. Or, for example, EIP (or its senior executive officers) may have
business or personal relationships with corporate directors or candidates for
directorship.

EIP addresses these conflicts or appearances of conflicts by ensuring that
proxies are voted in accordance with the recommendations made by RiskMetrics, an
independent third party proxy voting service. As previously noted, in most
cases, proxies will be voted in accordance with RiskMetrics's own pre-existing
proxy voting guidelines.

DISCLOSURE ON HOW PROXIES WERE VOTED

EIP will disclose to clients in its Form ADV how clients can obtain
information on how their proxies were voted, by contacting EIP at its office in
Westport, CT. EIP will also disclose in the ADV a summary of these proxy voting
policies and procedures and that upon request, clients will be furnished a full
copy of these policies and procedures.

It is the responsibility of the CCO to ensure that any requests made by
clients for proxy voting information are responded to in a timely fashion and
that a record of requests and responses are maintained in EIP's books and
records.

PROXY MATERIALS

EIP personnel will instruct custodians to forward to RiskMetrics all proxy
materials received on securities held in EIP client accounts.

LIMITATIONS

In certain circumstances, where EIP has determined that it is consistent
with the client's best interest, EIP will not take steps to ensure that proxies
are voted on securities in the client's account. The following are circumstances
where this may occur:

*Limited Value: Proxies will not be required to be voted on securities in
a client's account if the value of the client's economic interest in the
securities is indeterminable or insignificant (less than $1,000). Proxies will
also not be required to be voted for any securities that are no longer held by
the client's account.

*Securities Lending Program: When securities are out on loan, they are
transferred into the borrower's name and are voted by the borrower, in its
discretion. In most cases, EIP will not take steps to see that loaned securities
are voted. However, where EIP determines that a proxy vote, or other shareholder
action, is materially important to the client's account, EIP will make a good
faith effort to recall the security for purposes of voting, understanding that
in certain cases, the attempt to recall the security may not be effective in
time for voting deadlines to be met.

*Unjustifiable Costs: In certain circumstances, after doing a cost-benefit
analysis, EIP may choose not to vote where the cost of voting a client's proxy
would exceed any anticipated benefits to the client of the proxy proposal.

OVERSIGHT OF POLICY

The CCO is responsible for overseeing these proxy voting policies and
procedures. In addition, the CCO will review these policies and procedures not
less than annually with a view to determining whether their implementation has
been effective and that they are operating as intended and in such a fashion as
to maintaining EIP's compliance with all applicable requirements.

RECORDKEEPING ON PROXIES

In it the responsibility of EIP's CCO to ensure that the following proxy
voting records are maintained:

o a copy of EIP's proxy voting policies and procedures;

o a copy of all proxy statements received on securities in client
accounts (EIP may rely on RiskMetrics or the SEC's EDGAR system to
satisfy this requirement);

o a record of each vote cast on behalf of a client (EIP relies on
RiskMetrics to satisfy this requirement);

o a copy of any document prepared by EIP that was material to making a
voting decision or that memorializes the basis for that decision;

o a copy of each written client request for information on how proxies
were voted on the client's behalf or for a copy of EIP's proxy
voting policies and procedures, and

o a copy of any written response to any client request for information
on how proxies were voted on their behalf or furnishing a copy of
EIP's proxy voting policies and procedures.

The CCO will see that these books and records are made and maintained in
accordance with the requirements and time periods provided in Rule 204-2 of the
Advisers Act.

For any registered investment companies advised by EIP, votes made on its
behalf will be stored electronically or otherwise recorded so that they are
available for preparation of the Form N-PX, Annual Report of Proxy Voting Record
of Registered Management Investment Company.

ITEM 8. PORTFOLIO MANAGERS OF CLOSED-END MANAGEMENT INVESTMENT COMPANIES.

(A)(1) IDENTIFICATION OF PORTFOLIO MANAGER(S) OR MANAGEMENT TEAM MEMBERS AND
DESCRIPTION OF ROLE OF PORTFOLIO MANAGER(S) OR MANAGEMENT TEAM MEMBERS

Information provided as of February 6, 2013.

James Murchie, Chief Executive Officer and Founder of Energy Income Partners,
LLC ("EIP" or "Sub-Advisor"), and Eva Pao, principal of EIP, are co-portfolio
managers responsible for the day-to-day management of the registrant's
portfolio. Both portfolio managers have served in such capacity since the Fund's
inception.

JAMES J. MURCHIE
Founder and CEO of Energy Income Partners, LLC

Mr. Murchie founded EIP in 2003 and is the portfolio manager for all funds
advised by EIP which focus on energy-related master limited partnerships, income
trusts and similar securities. From 2005 to mid-2006, Mr. Murchie and the EIP
investment team joined Pequot Capital Management. In July 2006, Mr. Murchie and
the EIP investment team left Pequot and re-established EIP. From 1998 to 2003,
Mr. Murchie managed a long/short fund that invested in energy and cyclical
equities and commodities. From 1995 to 1997, he was a managing director at Tiger
Management where his primary responsibilities were investments in energy,
commodities and related equities. From 1990 to 1995, Mr. Murchie was a principal
at Sanford C. Bernstein where he was a top-ranked energy analyst and sat on the
Research Department's Recommendation Review Committee. Before joining Bernstein,
he spent eight years at British Petroleum in seven operating and staff positions
of increasing responsibility. He has served on the board of Clark Refining and
Marketing Company and as President and Treasurer of the Oil Analysts Group of
New York. Mr. Murchie holds degrees from Rice University and Harvard University.

EVA PAO
Principal of Energy Income Partners, LLC

Ms. Pao has been with EIP since its inception in 2003 and is co-portfolio
manager for all of the funds advised by EIP. She joined EIP in 2003, serving as
Managing Director of EIP until the EIP investment team joined Pequot Capital
Management. From 2005 to mid-2006, Ms. Pao served as Vice President of Pequot
Capital Management. Prior to Harvard Business School, Ms. Pao was a Manager at
Enron Corp where she managed a portfolio in Canadian oil and gas equities for
Enron's internal hedge fund that specialized in energy-related equities and
managed a natural gas trading book. She received a B.A. from Rice University in
1996. She received an M.B.A. from the Harvard Business School in 2002.

(A)(2) OTHER ACCOUNTS MANAGED BY PORTFOLIO MANAGER AND POTENTIAL CONFLICTS OF
INTEREST

OTHER ACCOUNTS MANAGED BY PORTFOLIO MANAGER

Information provided as of November 30, 2011.

------------------------- ----------------- -------------- --------------- ------------------------ -----------------------

Total # of # of Accounts Managed Total Assets for which
Name of Portfolio Type of Accounts Total Assets for which Advisory Fee Advisory Fee is Based
Manager or Accounts Managed (millions) is Based on on Performance
Team Member Performance (millions)
------------------------- ----------------- -------------- --------------- ------------------------ -----------------------
1. James Murchie Registered 4 $2170 0 $0
Investment
Companies:
------------------------- ----------------- -------------- --------------- ------------------------ -----------------------
Other Pooled
Investment
Vehicles: 3 $177 3 $177
------------------------- ----------------- -------------- --------------- ------------------------ -----------------------
Other Accounts: 635 $473 2 $45
------------------------- ----------------- -------------- --------------- ------------------------ -----------------------
Registered
Investment
2. Eva Pao Companies: 4 $2170 0 $0
------------------------- ----------------- -------------- --------------- ------------------------ -----------------------
Other Pooled
Investment
Vehicles: 3 $177 3 $177
------------------------- ----------------- -------------- --------------- ------------------------ -----------------------
Other Accounts: 635 $473 2 $45
------------------------- ----------------- -------------- --------------- ------------------------ -----------------------

POTENTIAL CONFLICTS OF INTERESTS

The EIP investment professionals that serve as portfolio managers of the
registrant also serve as portfolio managers to three private investment funds
(the "Private Funds"), each of which has a performance-based fee, one open-ended
mutual fund, and 510 separately managed accounts, 2 of which have a
performance-based fee.

EIP has written policies and procedures regarding Order Aggregation and
Allocation to ensure that all accounts are treated fairly and equitably and that
no account is disadvantaged. EIP will generally execute client transactions on
an aggregated basis when the Firm believes that to do so will allow it to obtain
best execution and to negotiate more favorable commission rates or avoid certain
transaction costs that might have otherwise been paid had such orders been
placed independently. EIP's ability to implement this may be limited by an
Account's custodian, directed brokerage arrangements or other constraints
limiting EIP's use of a common executing broker.

An aggregated order may be allocated on a basis different from that specified
herein provided all clients receive fair and equitable treatment and there is a
legitimate reason for the different allocation. Reasons for deviation may
include (but are not limited to): a client's investment guidelines and
restrictions, available cash, liquidity requirements, leverage targets,
rebalancing total risk exposure across all clients, tax or legal reasons, and to
avoid odd-lots or in cases when a normal allocation would result in a de minimis
allocation to one or more clients.

(A)(3) COMPENSATION STRUCTURE OF PORTFOLIO MANAGER(S) OR MANAGEMENT TEAM MEMBERS

Information provided as of November 30, 2012.

The portfolio managers are compensated by a competitive minimum base salary and
share in the profits of EIP in relationship to their ownership of EIP. The
profits of EIP are influenced by the assets managed by the funds and the
performance of the funds. While a portion of the portfolio manager's
compensation is tied to performance through incentive fees earned through the
private funds, the portfolio managers are not incentivized to take undue risk in
circumstances when the funds' performance lags as their investment fees may
sometimes have a high water mark or be subject to a hurdle rate. Moreover, the
Registrant's portfolio managers are the principal owners of EIP and are
incentivized to maximize the long-term performance of all of its funds. The
compensation of the Portfolio team members is determined according to prevailing
rates within the industry for similar positions. EIP wishes to attract, retain
and reward high quality personnel through competitive compensation.

(A)(4) DISCLOSURE OF SECURITIES OWNERSHIP

Information provided as of November 30, 2012.

Dollar Range of Fund Shares
Name Beneficially Owned
--------------- ---------------------------
James Murchie $0
Eva Pao $0

(B) Not applicable.

ITEM 9. PURCHASES OF EQUITY SECURITIES BY CLOSED-END MANAGEMENT INVESTMENT
COMPANY AND AFFILIATED PURCHASERS.

Not applicable.

ITEM 10. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.

There have been no material changes to the procedures by which the shareholders
may recommend nominees to the Registrant's board of trustees, where those
changes were implemented after the Registrant last provided disclosure in
response to the requirements of Item 407(c)(2)(iv) of Regulation S-K (17 CFR
229.407) (as required by Item 22(b)(15) of Schedule 14A (17 CFR 240.14a-101)),
or this Item.

ITEM 11. CONTROLS AND PROCEDURES.

(a) The Registrant's principal executive and principal financial officers, or
persons performing similar functions, have concluded that the
Registrant's disclosure controls and procedures (as defined in Rule
30a-3(c) under the Investment Company Act of 1940, as amended (the "1940

Act") (17 CFR 270.30a-3(c))) are effective, as of a date within 90 days
of the filing date of the report that includes the disclosure required by
this paragraph, based on their evaluation of these controls and
procedures required by Rule 30a-3(b) under the 1940 Act (17 CFR
270.30a-3(b)) and Rules 13a-15(b) or 15d-15(b) under the Securities
Exchange Act of 1934, as amended (17 CFR 240.13a-15(b) or 240.15d-15(b)).

(b) There were no changes in the Registrant's internal control over financial
reporting (as defined in Rule 30a-3(d) under the 1940 Act (17 CFR
270.30a-3(d)) that occurred during the Registrant's second fiscal quarter
of the period covered by this report that has materially affected, or is
reasonably likely to materially affect, the Registrant's internal control
over financial reporting.

ITEM 12. EXHIBITS.

(a)(1) Code of ethics, or any amendment thereto, that is the subject of
disclosure required by Item 2 is attached hereto.

(a)(2) Certifications pursuant to Rule 30a-2(a) under the 1940 Act and
Section 302 of the Sarbanes-Oxley Act of 2002 are attached hereto.

(a)(3) Not applicable.

(b) Certifications pursuant to Rule 30a-2(b) under the 1940 Act and
Section 906 of the Sarbanes- Oxley Act of 2002 are attached hereto.

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the registrant has duly caused this report to be
signed on its behalf by the undersigned, thereunto duly authorized.

(registrant) First Trust Energy Infrastructure Fund
-------------------------------------------------

By (Signature and Title)* /s/ Mark R. Bradley
----------------------------------------
Mark R. Bradley, President and
Chief Executive Officer
(principal executive officer)

Date January 28, 2013
---------------------

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, this report has been signed below by the
following persons on behalf of the registrant and in the capacities and on the
dates indicated.

By (Signature and Title)* /s/ Mark R. Bradley
----------------------------------------
Mark R. Bradley, President and
Chief Executive Officer
(principal executive officer)

Date January 28, 2013
---------------------

By (Signature and Title)* /s/ James M. Dykas
----------------------------------------
James M. Dykas, Treasurer,
Chief Financial Officer and
Chief Accounting Officer
(principal financial officer)

Date January 28, 2013
---------------------

* Print the name and title of each signing officer under his or her signature.