EXHIBIT 31.2

CERTIFICATION PURSUANT TOFORM OF RULE
13a-14(a)AND 15d-14(a)AS ADOPTED PURSUANT TOSECTION 302(A) OF THE
SARBANES-OXLEY ACT OF 2002

I, David L. Greenwood, Chief Financial
Officer of Geron Corporation, certify that:

|1. |  | I have reviewed this
      quarterly report on Form 10-Q of Geron Corporation;                                                                                                                                                                                                                                                                                       
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|   |  |                                                                                                                                                                                                                                                                                                                                                                      
|2. |  | Based on my knowledge,
      this report does not contain any untrue statement of a material fact or
      omit to state a material fact necessary to make the statements made, in
      light of the circumstances under which such statements were made, not
      misleading with respect to the period covered by this report;                                   
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|3. |  | Based on my knowledge,
      the financial statements, and other financial information included in this
      report, fairly present in all material respects the financial condition,
      results of operations and cash flows of the registrant as of, and for, the
      periods presented in this report;                                                      
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|4. |  | The registrants other
      certifying officer(s) and I are responsible for establishing and
      maintaining disclosure controls and procedures (as defined in Exchange Act
      Rules 13a-15(e) and 15d-15(e)) and internal control over financial
      reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for
      the registrant and have:
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|   |  | (a)                                                                                                                                                                                                                                                                                                                                                                  
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|   |  | (b)                                                                                                                                                                                                                                                                                                                                                                  
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|   |  | (c)                                                                                                                                                                                                                                                                                                                                                                  
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|   |  | (d)                                                                                                                                                                                                                                                                                                                                                                  
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|5. |  | The registrants other
      certifying officer(s) and I have disclosed, based on our most recent
      evaluation of internal control over financial reporting, to the
      registrants auditors and the audit committee of the registrants board of
      directors (or persons performing the equivalent functions):                                           
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|   |  | (a)                                                                                                                                                                                                                                                                                                                                                                  
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|   |  | (b)                                                                                                                                                                                                                                                                                                                                                                  

Date: October 31, 2008

|/s/ DAVID L. GREENWOOD                                     | 
|---------------------------------------------------------- | 
|David L.
      Greenwood                                  
|Executive
      Vice President and Chief Financial Officer

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