EXHIBIT 32.1

CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350,
AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

        In connection with the Annual Report on Form 10-K of World Heart Corporation (the "Corporation") for the year ended December 31, 2009, as filed with the Securities and Exchange Commission on the date hereof (the "Report"), the undersigned, John Alexander Martin, President and Chief Executive Officer of the Corporation, hereby certifies, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to his knowledge:

(1)

The Report fully complies with the requirements of Section 13(a) or 15(d) 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 Corporation as of December 31, 2009.

*

A signed original of this written statement required by section 906 has been provided to the Corporation and will be retained by the Corporation and furnished to the Securities and Exchange Commission or its staff upon request.

This certification accompanies the Form 10-K to which it relates, is not deemed filed with the Securities and Exchange Commission and is not to be incorporated by reference into any filing of the Corporation under the Securities Act of 1933, as amended, or the Securities Exchange Act of 1934, as amended (whether made before or after the date of the Form 10-K), irrespective of any general incorporation language contained in such filing.

QuickLinks

EXHIBIT 32.1