Exhibit 32.1

CERTIFICATIONS OF CHIEF EXECUTIVE OFFICER

UNDER

SECTION 906 OF THE SARBANES-OXLEY ACT

PACIFIC MERCANTILE BANCORP

Quarterly Report on Form 10-Q

for the quarter ended March 31, 2021

In connection with the accompanying Quarterly Report on Form 10-Q of Pacific Mercantile Bancorp (the “Company”) for the quarter ended March 31, 2021 (the “Quarterly Report”), and pursuant to 18 U.S.C. §1350, as adopted pursuant to §906 of the Sarbanes-Oxley Act of 2003, I, Bradford R. Dinsmore, certify that:

(1) The Quarterly Report fully complies with the requirements of Section 13(a) and 15(d) of the Securities Exchange Act of 1934; and

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

Dated: May 7, 2021

/S/    BRADFORD R. DINSMORE

Bradford R. Dinsmore

President and Chief Executive Officer