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

                                    FORM N-Q

       QUARTERLY SCHEDULE OF PORTFOLIO HOLDINGS OF REGISTERED MANAGEMENT
                               INVESTMENT COMPANY

                  Investment Company Act file number 811-22528
                                                    -----------

                     First Trust Energy Infrastructure Fund
        ----------------------------------------------------------------
               (Exact name of registrant as specified in charter)

                       120 East Liberty Drive, Suite 400
                               Wheaton, IL 60187
        ----------------------------------------------------------------
              (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
        ----------------------------------------------------------------
                    (Name and address of agent for service)

        Registrant's telephone number, including area code: 630-765-8000
                                                           --------------

                      Date of fiscal year end: November 30
                                              -------------

                   Date of reporting period: February 28, 2015
                                             -----------------

Form N-Q is to be used by management investment companies, other than small
business investment companies registered on Form N-5 (ss.ss. 239.24 and 274.5 of
this chapter), to file reports with the Commission, not later than 60 days after
the close of the first and third fiscal quarters, pursuant to rule 30b1-5 under
the Investment Company Act of 1940 (17 CFR 270.30b1-5). The Commission may use
the information provided on Form N-Q in its regulatory, disclosure review,
inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-Q, and
the Commission will make this information public. A registrant is not required
to respond to the collection of information contained in Form N-Q 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 the
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. SCHEDULE OF INVESTMENTS. The Schedule(s) of Investments is attached
herewith.


FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS
FEBRUARY 28, 2015 (UNAUDITED)





     SHARES                                     DESCRIPTION                                    VALUE
---------------  --------------------------------------------------------------------      --------------

COMMON STOCKS - 92.3%

                                                                                     
                 ELECTRIC UTILITIES - 16.2%
         72,400  American Electric Power Co., Inc. (a)...............................      $    4,168,792
         38,200  Duke Energy Corp. ..................................................           3,000,610
        176,400  Emera, Inc. (CAD) (a)...............................................           5,781,224
        241,600  Eversource Energy (a)...............................................          12,502,800
        168,700  Exelon Corp. (a)....................................................           5,722,304
        176,800  Fortis, Inc. (CAD) (a)..............................................           5,597,747
         60,000  IDACORP, Inc. (a)...................................................           3,757,200
        280,800  ITC Holdings Corp. (a)..............................................          10,875,384
         93,300  NextEra Energy, Inc. (a)............................................           9,652,818
        104,300  NRG Yield, Inc., Class A (a)........................................           5,351,633
        117,900  Southern (The) Co. (a)..............................................           5,398,641
                                                                                           --------------
                                                                                               71,809,153
                                                                                           --------------

                 GAS UTILITIES - 7.8%
        111,800  Atmos Energy Corp. (a)..............................................           5,929,872
         27,810  Chesapeake Utilities Corp. (a)......................................           1,312,632
        161,000  ONE Gas, Inc. (a)...................................................           6,699,210
        150,000  Piedmont Natural Gas Co., Inc. .....................................           5,595,000
         69,000  South Jersey Industries, Inc. (a)...................................           3,910,920
        323,718  UGI Corp. (a).......................................................          11,003,175
                                                                                           --------------
                                                                                               34,450,809
                                                                                           --------------

                 INDEPENDENT POWER AND RENEWABLE ELECTRICITY PRODUCERS - 0.9%
        137,000  Pattern Energy Group, Inc. (a)......................................           3,811,340
                                                                                           --------------

                 MULTI-UTILITIES - 16.3%
         49,000  Alliant Energy Corp. (a)............................................           3,116,400
        142,200  ATCO, Ltd., Class I (CAD) (a).......................................           5,486,206
        191,000  Canadian Utilities Ltd., Class A (CAD) (a)..........................           6,348,332
        116,000  CMS Energy Corp. (a)................................................           4,075,080
        113,900  Dominion Resources, Inc. (a)........................................           8,211,051
         64,000  National Grid PLC, ADR .............................................           4,387,840
        222,900  NiSource, Inc. (a)..................................................           9,564,639
        229,000  Public Service Enterprise Group, Inc. ..............................           9,631,740
         85,000  SCANA Corp. ........................................................           4,840,750
         56,000  Sempra Energy (a)...................................................           6,059,200
        205,100  Wisconsin Energy Corp. (a)..........................................          10,455,998
                                                                                           --------------
                                                                                               72,177,236
                                                                                           --------------

                 OIL, GAS & CONSUMABLE FUELS - 50.2%
      1,425,938  Enbridge Energy Management, LLC (a) (b).............................          53,158,969
        458,600  Enbridge Income Fund Holdings, Inc. (CAD) (a).......................          14,475,927
        264,169  Enbridge, Inc. (a)..................................................          12,268,008
        422,000  Inter Pipeline, Ltd. (CAD) (a)......................................          11,207,423
         90,300  Keyera Corp. (CAD) (a)..............................................           6,048,171
      1,347,875  Kinder Morgan, Inc. (a).............................................          55,276,354
        150,000  ONEOK, Inc. ........................................................           6,639,000
        153,100  Pembina Pipeline Corp. (CAD) (a)....................................           4,896,359
        434,400  Spectra Energy Corp. (a)............................................          15,416,856
        495,700  TransCanada Corp. (a)...............................................          21,726,531



Page 1          See Notes to Quarterly Portfolio of Investments



FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
FEBRUARY 28, 2015 (UNAUDITED)





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

COMMON STOCKS (CONTINUED)

                                                                                     
                 OIL, GAS & CONSUMABLE FUELS (CONTINUED)
        434,600  Williams (The) Cos., Inc. (a).......................................      $   21,312,784
                                                                                           --------------
                                                                                              222,426,382
                                                                                           --------------

                 REAL ESTATE INVESTMENT TRUSTS - 0.9%
        135,000  CorEnergy Infrastructure Trust .....................................             907,200
        109,150  InfraREIT, Inc. ....................................................           2,960,148
                                                                                           --------------
                                                                                                3,867,348
                                                                                           --------------
                 TOTAL COMMON STOCKS ................................................         408,542,268
                 (Cost $347,793,510)                                                       --------------

MASTER LIMITED PARTNERSHIPS - 35.0%

                 GAS UTILITIES - 3.6%
        263,752  AmeriGas Partners, L.P. (a).........................................          12,984,511
         67,000  Suburban Propane Partners, L.P. (a).................................           2,957,380
                                                                                           --------------
                                                                                               15,941,891
                                                                                           --------------

                 INDEPENDENT POWER AND RENEWABLE ELECTRICITY PRODUCERS - 0.8%
         84,300  NextEra Energy Partners, L.P. (a)...................................           3,325,635
                                                                                           --------------

                 OIL, GAS & CONSUMABLE FUELS - 30.6%
         46,000  Alliance Holdings GP, L.P. (a)......................................           2,417,300
        219,430  Alliance Resource Partners, L.P. (a)................................           8,678,457
         34,200  Columbia Pipeline Partners, L.P. (c)................................             946,998
         97,000  Energy Transfer Equity, L.P. (a)....................................           6,195,390
        285,400  Energy Transfer Partners, L.P. (a)..................................          16,975,592
        241,200  Enterprise Products Partners, L.P. (a)..............................           8,041,608
         89,700  EQT Midstream Partners, L.P. (a)....................................           7,464,834
        180,539  Golar LNG Partners, L.P. (a)........................................           4,713,873
         19,800  Hoegh LNG Partners, L.P. ...........................................             444,510
        208,876  Holly Energy Partners, L.P. (a).....................................           6,945,127
         70,600  Magellan Midstream Partners, L.P. (a)...............................           5,803,320
        201,239  Natural Resource Partners, L.P. (a).................................           1,595,825
        178,172  NGL Energy Partners, L.P. (a).......................................           5,437,809
        190,200  ONEOK Partners, L.P. (a)............................................           7,948,458
         47,100  Phillips 66 Partners, L.P. (a)......................................           3,353,049
        173,486  Plains All American Pipeline, L.P. (a)..............................           8,655,217
         18,600  Shell Midstream Partners, L.P. (a)..................................             726,516
        141,900  Spectra Energy Partners, L.P. (a)...................................           7,568,946
         20,000  Targa Resources Partners, L.P. .....................................             876,400
        125,095  TC Pipelines, L.P. (a)..............................................           8,253,768
        159,628  Teekay LNG Partners, L.P. (a).......................................           5,914,217
        175,762  TransMontaigne Partners, L.P. (a)...................................           6,255,370
        201,938  Williams Partners, L.P. (a).........................................          10,327,109
                                                                                           --------------
                                                                                              135,539,693
                                                                                           --------------
                 TOTAL MASTER LIMITED PARTNERSHIPS ..................................         154,807,219
                 (Cost $126,954,451)                                                       --------------

                 TOTAL INVESTMENTS - 127.3% .........................................         563,349,487
                 (Cost $474,747,961) (d)                                                   --------------



Page 2          See Notes to Quarterly Portfolio of Investments



FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
FEBRUARY 28, 2015 (UNAUDITED)





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

CALL OPTIONS WRITTEN - (0.3%)

                                                                                     
                 American Electric Power Co., Inc. Calls
            420  @   $65.00 due March 2015 (e).......................................      $       (1,260)
             20  @    65.00 due May 2015.............................................                (300)
                                                                                           --------------
                                                                                                   (1,560)
                                                                                           --------------
                 CMS Energy Corp. Call
            710  @    40.00 due June 2015............................................             (19,525)
                                                                                           --------------
                 Dominion Resources, Inc. Calls
            630  @    77.50 due April 2015...........................................             (16,380)
             70  @    82.50 due April 2015...........................................                (350)
                                                                                           --------------
                                                                                                  (16,730)
                                                                                           --------------
                 Duke Energy Corp. Call
            230  @    87.50 due April 2015...........................................              (1,150)
                                                                                           --------------
                 Enbridge, Inc. Call
          1,630  @    55.00 due April 2015 (e).......................................             (37,490)
                                                                                           --------------
                 Eversource Energy Call
          1,490  @    55.00 due April 2015...........................................             (52,150)
                                                                                           --------------
                 Exelon Corp. Calls
          1,030  @    37.00 due April 2015...........................................             (11,330)
            350  @    39.00 due April 2015 (e).......................................                (700)
                                                                                           --------------
                                                                                                  (12,030)
                                                                                           --------------
                 IDACORP, Inc. Calls
            100  @    70.00 due August 2015..........................................              (8,000)
            270  @    75.00 due August 2015..........................................              (7,425)
                                                                                           --------------
                                                                                                  (15,425)
                                                                                           --------------
                 Kinder Morgan, Inc. Calls
            300  @    40.00 due March 2015...........................................             (40,500)
          2,750  @    42.50 due March 2015...........................................             (41,250)
          2,190  @    45.00 due March 2015...........................................              (4,380)
                                                                                           --------------
                                                                                                  (86,130)
                                                                                           --------------
                 National Grid PLC, ADR Call
            390  @    75.00 due March 2015 (e).......................................              (5,070)
                                                                                           --------------
                 NextEra Energy Partners, L.P. Call
            570  @    120.00 due September 2015......................................             (49,875)
                                                                                           --------------
                 NiSource, Inc. Calls
            320  @    45.00 due April 2015...........................................             (14,400)
          1,060  @    47.00 due July 2015............................................             (68,900)
                                                                                           --------------
                                                                                                  (83,300)
                                                                                           --------------



Page 3          See Notes to Quarterly Portfolio of Investments



FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
FEBRUARY 28, 2015 (UNAUDITED)





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

CALL OPTIONS WRITTEN (CONTINUED)

                                                                                     
                 ONE Gas, Inc. Calls
            590  @   $40.00 due April 2015...........................................      $     (169,625)
            400  @    50.00 due July 2015............................................             (25,000)
                                                                                           --------------
                                                                                                 (194,625)
                                                                                           --------------
                 ONEOK, Inc. Calls
            600  @    50.00 due April 2015...........................................             (16,500)
            330  @    50.00 due July 2015............................................             (29,040)
                                                                                           --------------
                                                                                                  (45,540)
                                                                                           --------------
                 Plains All American Pipeline, L.P. Call
            450  @    55.00 due August 2015..........................................             (40,950)
                                                                                           --------------
                 Public Service Enterprise Group, Inc. Calls
            700  @    40.00 due March 2015...........................................            (129,500)
            370  @    45.00 due March 2015 (e).......................................              (4,810)
            570  @    45.00 due April 2015...........................................             (11,400)
                                                                                           --------------
                                                                                                 (145,710)
                                                                                           --------------
                 SCANA Corp. Call
            520  @    65.00 due August 2015..........................................             (23,400)
                                                                                           --------------
                 Sempra Energy Call
            340  @    125.00 due July 2015...........................................              (6,800)
                                                                                           --------------
                 Southern (The) Co. Calls
            530  @    50.00 due May 2015.............................................              (9,540)
            200  @    55.00 due May 2015.............................................                (600)
                                                                                           --------------
                                                                                                  (10,140)
                                                                                           --------------
                 Spectra Energy Corp. Calls
          1,200  @    37.00 due March 2015...........................................             (21,000)
            160  @    38.00 due April 2015...........................................              (3,200)
          1,330  @    38.00 due June 2015............................................             (66,500)
                                                                                           --------------
                                                                                                  (90,700)
                                                                                           --------------
                 TransCanada Corp. Calls
            500  @    50.00 due March 2015 (e).......................................              (5,000)
            500  @    50.00 due May 2015 (e).........................................             (12,500)
            800  @    55.00 due May 2015 (e).........................................              (4,800)
          1,270  @    50.00 due August 2015..........................................             (69,850)
                                                                                           --------------
                                                                                                  (92,150)
                                                                                           --------------
                 UGI Corp. Call
          2,565  @    40.00 due April 2015 (e).......................................             (89,775)
                                                                                           --------------
                 Williams (The) Cos., Inc. Calls
            500  @    48.00 due March 2015...........................................             (70,000)
            754  @    52.50 due April 2015...........................................             (25,636)
                                                                                           --------------
                                                                                                  (95,636)



Page 4          See Notes to Quarterly Portfolio of Investments



FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
FEBRUARY 28, 2015 (UNAUDITED)





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

CALL OPTIONS WRITTEN (CONTINUED)

                                                                                     
                 Wisconsin Energy Corp. Call
          1,580  @   $60.00 due July 2015............................................      $      (27,650)
                                                                                           --------------
                 TOTAL CALL OPTIONS WRITTEN .........................................          (1,243,511)
                 (Premiums received $1,620,845)                                            --------------

                 OUTSTANDING LOAN - (34.1%) .........................................        (151,000,000)

                 NET OTHER ASSETS AND LIABILITIES - 7.1% ............................          31,599,526
                                                                                           --------------
                 NET ASSETS - 100.0% ................................................      $  442,705,502
                                                                                           ==============


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

      (a) All or a portion of this security serves as collateral on the
          outstanding loan.

      (b) Non-income producing security which pays in-kind ("PIK")
          distributions. For the fiscal year-to-date period (December 1, 2014
          through February 28, 2015), the Fund received 21,350 PIK shares of
          Enbridge Energy Management, LLC.

      (c) Non-income producing security.

      (d) Aggregate cost for financial reporting purposes, which approximates
          the aggregate cost for federal income tax purposes. As of February 28,
          2015, the aggregate gross unrealized appreciation for all securities
          in which there was an excess of value over tax cost was $98,645,790
          and the aggregate gross unrealized depreciation for all securities in
          which there was an excess of tax cost over value was $10,044,264.

      (e) This security is fair valued by the Advisor's Pricing Committee in
          accordance with procedures adopted by the Fund's Board of Trustees and
          in accordance with provisions of the Investment Company Act of 1940,
          as amended. At February 28, 2015, securities noted as such are valued
          at $(161,405) or (0.04%) of net assets.

     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.


INTEREST RATE SWAP AGREEMENTS:


                                                               NOTIONAL
     COUNTERPARTY      FLOATING RATE(1)   EXPIRATION DATE       AMOUNT      FIXED RATE(1)       VALUE
---------------------------------------------------------------------------------------------------------
                                                                             
Bank of Nova Scotia    1 month LIBOR          10/08/20      $   36,475,000      2.121%      $ (1,122,049)
Bank of Nova Scotia    1 month LIBOR          09/03/24          36,475,000      2.367%        (1,443,503)
                                                            --------------                  ------------
                                                            $   72,950,000                  $ (2,565,552)
                                                            ==============                  ============



(1) The Fund pays the fixed rate and receives the floating rate. The floating
rate on February 28, 2015 was 0.17%.


Page 5          See Notes to Quarterly Portfolio of Investments



FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
PORTFOLIO OF INVESTMENTS (CONTINUED)
FEBRUARY 28, 2015 (UNAUDITED)



VALUATION INPUTS
A summary of the inputs used to value the Fund's investments as of February 28,
2015 is as follows (see Note 2A - Portfolio Valuation in the Notes to Quarterly
Portfolio of Investments):



                                                  ASSETS TABLE
                                                                                          LEVEL 2            LEVEL 3
                                                     TOTAL                              SIGNIFICANT        SIGNIFICANT
                                                    VALUE AT        LEVEL 1 QUOTED       OBSERVABLE        UNOBSERVABLE
                                                   2/28/2015            PRICES             INPUTS             INPUTS
                                                ----------------   ----------------   ----------------   ----------------
                                                                                             
Common Stocks*................................  $   408,542,268    $   408,542,268    $             --   $           --
Master Limited Partnerships *.................      154,807,219        154,807,219                  --               --
                                                ---------------    ---------------    ----------------   --------------
TOTAL ........................................  $   563,349,487    $   563,349,487    $             --   $           --
                                                ===============    ===============    ================   ==============

                                               LIABILITIES TABLE
                                                                                          LEVEL 2            LEVEL 3
                                                     TOTAL                              SIGNIFICANT        SIGNIFICANT
                                                    VALUE AT        LEVEL 1 QUOTED       OBSERVABLE        UNOBSERVABLE
                                                   2/28/2015            PRICES             INPUTS             INPUTS
                                                ----------------   ----------------   ----------------   ----------------
Call Options Written..........................  $    (1,243,511)   $    (1,082,106)  $        (161,405)  $           --
Interest Rate Swaps** ........................       (2,565,552)                --          (2,565,552)              --
                                                ---------------    ---------------   -----------------   --------------
TOTAL ........................................  $    (3,809,063)   $    (1,082,106)  $      (2,726,957)  $           --
                                                ===============    ===============   =================   ==============


*   See Portfolio of Investments for industry breakout.
**  See Interest Rate Swap Agreements for contract detail.

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. There were no
transfers between Levels at February 28, 2015.


Page 6          See Notes to Quarterly Portfolio of Investments




NOTES TO QUARTERLY PORTFOLIO OF INVESTMENTS

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         FEBRUARY 28, 2015 (UNAUDITED)


                                1. ORGANIZATION

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 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").


                     2. VALUATION AND INVESTMENT PRACTICES

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. Foreign securities are
priced using data reflecting the earlier closing of the principal markets for
those securities. 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 at market value or, in absence of market
value with respect to any portfolio securities, at fair value. Market value
prices represent last sale or official closing prices from a national or foreign
exchange (i.e., a regulated market) and are primarily obtained from third party
pricing services. Fair value prices represent any prices not considered market
value prices and are either obtained from a third party pricing service or are
determined by the Pricing Committee of the Fund's investment advisor, First
Trust Advisors L.P. (the "Advisor"), in accordance with valuation procedures
adopted by the Fund's Board of Trustees, and in accordance with provisions of
the 1940 Act. Investments valued by the Advisor's Pricing Committee, if any, are
footnoted as such in the footnotes to the Portfolio of Investments. The Fund's
investments are valued as follows:

      Common stocks, master limited partnerships ("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 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 contracts are fair valued at the mean
      of their most recent bid and asked price, if available, and otherwise at
      their closing bid price. Over-the-counter options contracts are fair
      valued at the mean of their most recent bid and asked price, if available,
      and otherwise at their closing bid price.

      Securities traded in an over-the-counter market are fair valued at the
      mean of their most recent bid and asked price, if available, and otherwise
      at their closing bid price.

      Swaps are fair valued utilizing quotations provided by a third party
      pricing service or, if the pricing service does not provide a value, by
      quotes provided by the selling dealer or financial institution.

Certain securities may not be able to be priced by pre-established pricing
methods. Such securities may be valued by the Fund's Board of Trustees or its
delegate, the Advisor's Pricing Committee, at fair value. These securities
generally include, but are not limited to, restricted securities (securities
which may not be publicly sold without registration under the Securities Act of
1933, as amended) for which a pricing service is unable to provide a market
price; securities whose trading has been formally suspended; a security whose
market or fair value price is not available from a pre-established pricing
source; a security with respect to which an event has occurred that is likely to
materially affect the value of the security after the market has closed but
before the calculation of the Fund's NAV or make it difficult or impossible to
obtain a reliable market quotation; and a security whose price, as provided by
the pricing service, does not reflect the security's fair value. As a general
principle, the current fair value of a security would appear to be the amount
which the owner might reasonably expect to receive for the security upon its
current sale. When fair value prices are used, generally they will differ from
market quotations or official closing prices on the applicable exchanges. A
variety of factors may be considered in determining the fair value of such
securities, 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 7


NOTES TO QUARTERLY PORTFOLIO OF INVESTMENTS (CONTINUED)

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         FEBRUARY 28, 2015 (UNAUDITED)


      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:

                o Quoted prices for similar investments in active markets.

                o 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.

                o 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).

                o 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 methodologies 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 Februray 28, 2015, 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 write (sell) options to hedge against changes in
the value of equities. Also, the Fund seeks to generate additional income, in
the form of premiums received, from writing (selling) the options. The Fund may
write (sell) covered call or put options ("options") on all or a portion of the
common stock and MLPs 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 and MLPs the Fund holds in its portfolio. The Fund will not write (sell)
"naked" or uncovered options. 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 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 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.

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


Page 8


NOTES TO QUARTERLY PORTFOLIO OF INVESTMENTS (CONTINUED)

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         FEBRUARY 28, 2015 (UNAUDITED)


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
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 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. SWAP AGREEMENTS:

The Fund may enter into total return equity swap and interest rate swap
agreements. A swap is a financial instrument that typically involves the
exchange of cash flows between two parties ("Counterparties") on specified dates
(settlement dates) where the cash flows are based on agreed upon prices, rates,
etc. Swap agreements are individually negotiated and involve the risk of the
potential inability of the Counterparties to meet the terms of the agreement. In
connection with these agreements, cash and securities may be identified as
collateral in accordance with the terms of the respective swap agreements to
provide assets of value and recourse in the event of default under the swap
agreement or bankruptcy/insolvency of a party to the swap agreement. In the
event of a default by the Counterparty, the Fund will seek withdrawal of this
collateral and may incur certain costs exercising its right with respect to the
collateral. If a Counterparty becomes bankrupt or otherwise fails to perform its
obligations due to financial difficulties, the Fund may experience significant
delays in obtaining any recovery in a bankruptcy or other reorganization
proceeding. The Fund may obtain only limited recovery or may obtain no recovery
in such circumstances.

Swap agreements may increase or decrease the overall volatility of the
investments of the Fund. The performance of swap agreements may be affected by a
change in the specific interest rate, security, currency, or other factors that
determine the amounts of payments due to and from the Fund. The Fund's maximum
equity price risk to meet its future payments under swap agreements outstanding
at February 28, 2015 is equal to the total notional amount as shown on the
Portfolio of Investments. The notional amount represents the U.S. dollar value
of the contract as of the day of the opening transaction or contract reset.

The Fund held interest rate swap agreements at February 28, 2015. An interest
rate swap agreement involves the Fund's agreement to exchange a stream of
interest payments for another party's stream of cash flows. Interest rate swaps
do not involve the delivery of securities or other underlying assets or
principal. Accordingly, the risk of loss with respect to interest rate swaps is
limited to the net amount of interest payments that the Fund is contractually
obligated to make.

D. SECURITIES TRANSACTIONS:

Securities transactions are recorded as of the trade date. Realized gains and
losses from securities transactions are recorded on the identified cost basis.

E. 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 investments and items of income and expense are
translated on the respective dates of such transactions.


Page 9


NOTES TO QUARTERLY PORTFOLIO OF INVESTMENTS (CONTINUED)

                  FIRST TRUST ENERGY INFRASTRUCTURE FUND (FIF)
                         FEBRUARY 28, 2015 (UNAUDITED)


                          3. DERIVATIVES TRANSACTIONS

Written option activity for the Fund for the fiscal year-to-date period
(December 1, 2014 through February 28, 2015) was as follows:

                                                    NUMBER
                                                      OF
WRITTEN OPTIONS                                    CONTRACTS      PREMIUMS
----------------------------------------------------------------------------

Options outstanding at November 30, 2014...           28,408   $   1,585,058
Options Written............................           38,709       2,151,030
Options Expired............................          (18,449)     (1,079,986)
Options Exercised..........................          (12,314)       (788,815)
Options Closed.............................           (5,065)       (246,442)
                                                 -----------   -------------
Options outstanding at February 28, 2015...           31,289   $   1,620,845
                                                 ===========   =============

The average volume of interest rate swaps was $72,950,000 for the fiscal
year-to-date period (December 1, 2014 through February 28, 2015).


Page 10




ITEM 2. 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 last fiscal quarter
       that have materially affected, or are reasonably likely to materially
       affect, the registrant's internal control over financial reporting.

ITEM 3. EXHIBITS.

Certifications pursuant to Rule 30a-2(a) under the 1940 Act and Section 302 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: April 17, 2015
     ---------------------

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: April 17, 2015
     ---------------------

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

Date: April 17, 2015
     ---------------------

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