Exhibit 32.1

Certification of Principal Executive Officer
Pursuant to 18 U.S.C. 1350
(Section 906 of the Sarbanes-Oxley Act of 2002)

I, William A. Haseltine, Ph.D., Chairman and Chief Executive Officer (principal executive officer) of Human Genome Sciences, Inc. (the “Registrant”), certify, to the best of my knowledge, based upon a review of the Quarterly Report on Form 10-Q for the period ended March 31, 2004 of the Registrant (the “Report”), that:

          (1)   The Report fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934, as amended; and

          (2)   The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Registrant.

/s/ William A. Haseltine, Ph.D.
Name:	William A. Haseltine, Ph.D.
Date:	May 7, 2004