<Page>

                                                                    EXHIBIT 23.1


                          INDEPENDENT AUDITORS' CONSENT


The Board of Directors
GenVec, Inc.:

We consent to the incorporation by reference in the registration statements (No.
333-101963) on Form S-3, in the registration statement (No. 333-76886) on Form
S-3/A, and in the registration statements (No. 333-55590, 333-55586 and No.
333-55584) on Form S-8 of GenVec, Inc. of our report dated March 13, 2003, with
respect to the balance sheets of GenVec, Inc. as of December 31, 2002 and 2001,
and the related statements of operations, stockholders' equity and cash flows
for each of the years in the three-year period ended December 31, 2002, which
report appears in the December 31, 2002 annual report on Form 10-K of GenVec,
Inc.


/s/ KPMG LLP



Baltimore, Maryland
March 27, 2003