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

PROSPECTUS SUPPLEMENT NO. 1
(TO PROSPECTUS DATED JANUARY 29, 2002)

GERON CORPORATION

COMMON STOCK,
WARRANTS TO PURCHASE COMMON STOCK AND
COMMON STOCK ISSUABLE UPON EXERCISE OF WARRANTS

     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 2,000,000 shares of our common stock, par value $0.001 per share, to Mainfield Enterprises, Inc., which we refer to as “Mainfield,” and we are offering an aggregate of 2,000,000 shares of our common stock to The Riverview Group, LLC, which we refer to as “Riverview.” The 4,000,000 shares of our common stock are being offered pursuant to the terms and conditions of a common stock purchase agreement among Mainfield, Riverview and the company at a price of $4.60 per share. The total purchase price for all of these shares of our common stock is $18,400,000. We would receive proceeds from the sale of these 4,000,000 shares equal to approximately $18,400,000 less our expenses relating to the sale, which are estimated to be $1,144,000. As part of the offer, Mainfield and Riverview would both receive a right of first offer on certain future issuances of our securities during the twelve months following the proposed transaction.

     In addition, if the volume-weighted average price on April 8, 2003 of our common stock reported on the Nasdaq National Market exceeds $4.75 per share, we could require each of Mainfield and Riverview to purchase 200,000 additional shares each of our common stock at a price of $4.60 per share. The total purchase price for the additional 400,000 shares of our common stock is $1,840,000. We would receive proceeds from the sale of these 400,000 shares equal to approximately $1,840,000 less our expenses relating to the sale, which are estimated to be $120,400.

S-1

     In connection with the sale of our common stock to Mainfield and Riverview, we would issue a warrant to purchase an aggregate of 300,000 shares of common stock to each of Mainfield and Riverview. The warrants to purchase a total of 600,000 shares would be exercisable, either in their entirety or partially from time to time, at a price of $6.34 per share for three years from the date of issuance; however, we could require Mainfield and Riverview to exercise the warrants if the volume-weighted average price of our common stock during a period of seven consecutive trading days reported on the Nasdaq National Market is equal to or greater than $9.64 per share. The total purchase price for all of these shares of our common stock is $3,804,000. We would receive proceeds from the sale of these 600,000 shares equal to approximately $3,804,000 less our expenses relating to the sale, which are estimated to be $15,000.

     Our common stock is quoted on the Nasdaq National Market under the symbol “GERN.” On April 7, 2003, the last reported sale price of our common stock on the Nasdaq National Market was $5.51 per share. As of April 1, 2003, we had 25,169,651 shares of common stock outstanding.

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

     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 April 7, 2003.

S-2

TABLE OF CONTENTS

PROSPECTUS

S-3