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;                                                                                                                                                                                                                                                                                     
|-- |  | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
|  
|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;                                 
|  
|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;                                                    
|  
|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:
|  
|   |  | (a)                                                                                                                                                                                                                                                                                                                                                                  
|  
|   |  | (b)                                                                                                                                                                                                                                                                                                                                                                  
|  
|   |  | (c)                                                                                                                                                                                                                                                                                                                                                                  
|  
|   |  | (d)                                                                                                                                                                                                                                                                                                                                                                  
|  
|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):                                       
|  
|   |  | (a)                                                                                                                                                                                                                                                                                                                                                                  
|  
|   |  | (b)                                                                                                                                                                                                                                                                                                                                                                  

|Date: April 30,
      2009                                
|----------------------------------------------------------
|                                                          
|/s/ DAVID L. GREENWOOD                                    
|David L.
      Greenwood                                  
|Executive Vice President
      and Chief Financial Officer

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