FILING PURSUANT TO RULE 424(b)(2)
                                            REGISTRATION STATEMENT NO. 333-81596



                           PROSPECTUS SUPPLEMENT NO. 2
                     (TO PROSPECTUS DATED JANUARY 29, 2002)

                                GERON CORPORATION

                                  COMMON STOCK


           You should read this prospectus supplement and the accompanying
prospectus carefully before you invest. Both documents contain information you
should consider carefully before making your investment decision.

           We are offering an aggregate of 310,000 shares of our common stock,
par value $0.001 per share, to Transgenomic, Inc., which we refer to as
"Transgenomic." The 310,000 shares of our common stock are being offered
pursuant to the terms and conditions of a common stock purchase agreement
between Transgenomic and the company at a price of $5.05 per share. The total
purchase price for all of these shares of our common stock is $1,565,500. We
would receive proceeds from the sale of these 310,000 shares equal to
approximately $1,565,500 less our expenses relating to the sale, which are
estimated to be $5,000.

           Transgenomic's purchase of our common stock is in connection with the
amendment of an existing license agreement under which Transgenomic is granted
the right to use certain patents owned or controlled by us in the manufacture of
products for the research market. The amendment broadens the field of the
license to include the manufacture of products for therapeutic or diagnostic
use. The license agreement also provides for Transgenomic to pay royalties to us
on sales of products manufactured under the license.

           Our common stock is quoted on the Nasdaq National Market under the
symbol "GERN." On June 2, 2003, the last reported sale price of our common stock
on the Nasdaq National Market was $5.05 per share. As of May 30, 2003, we had
29,608,055 shares of common stock outstanding.

           Investing in our common stock involves certain risks. See "Risk
Factors" beginning on page 2 of the prospectus.

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           You should rely on the information provided or incorporated by
reference in this prospectus supplement and the prospectus. We have not
authorized anyone else to provide you with different information. You should not
assume that the information in this prospectus supplement is accurate as of any
date other than the date on the front of these documents.

           Neither the U.S. Securities and Exchange Commission nor any state
securities commission has approved or disapproved of the securities or passed
upon the accuracy or adequacy of this prospectus. Any representation to the
contrary is a criminal offense.

           The date of this prospectus supplement is June 3, 2003.


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                                TABLE OF CONTENTS

                                   PROSPECTUS


About this Prospectus........................................1
About Geron..................................................2
Risk Factors.................................................2
Forward-Looking Statements...................................2
Ratio of Earnings to Fixed Charges..........................14
Use of Proceeds.............................................14
Plan of Distribution........................................15
Description of Debt Securities..............................16
Description of Common Stock.................................25
Description of Preferred Stock..............................26
Description of Warrants.....................................28
Certain Provisions of Delaware Law and
        of the Company's Charter and Bylaws.................29
Validity of Securities......................................30
Experts.....................................................30
Limitation on Liability and Disclosure of
        Commission Position on Indemnification for
        Securities Act Liabilities..........................30
Where You Can Find More Information.........................31


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