EXHIBIT 32.1

CERTIFICATION

PURSUANT TO 18 U.S.C. 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

I, Richard Murray, IV, Chairman of the Board and Chief Executive Officer of National Commerce Corporation, certify, pursuant to 18 U.S.C. 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that the Annual Report on Form 10-K of National Commerce Corporation for the fiscal year ended December 31, 2018, fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and the information contained in such Annual Report on Form 10-K fairly presents, in all material respects, the financial condition and results of operations of National Commerce Corporation.

/s/ Richard Murray, IV

Richard Murray, IV

Chairman of the Board and Chief Executive Officer

March 4, 2019