Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the inclusion in the Post-Effective Amendment No. 1 to the Registration Statement No. 333-244353 on Form S-1 of Compass Therapeutics, Inc. of our report dated March 5, 2021 on our audits of the consolidated financial statements of Compass Therapeutics, Inc. and Subsidiaries as of December 31, 2020 and 2019 and for the years then ended. We also consent to the reference to our firm under the heading “Experts.”

/s/ CohnReznick LLP

Hartford, Connecticut

March 5, 2021