Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

As independent registered public accountants, we hereby consent to the incorporation by reference in Registration Statement Nos. 333-194930, 333-202656, 333-206347, 333-212960, 333-218018, 333-227267 and 333-227900 on Forms S-8, Registration Statement Nos. 333-224946 and 333-220048 on Forms S-3, and Registration Statement No. 333-227908 on Form S-1 of our report dated March 28, 2019, relating to the financial statements of Biocept, Inc. (“Company”) (which includes explanatory paragraphs related to the change in the method of accounting for revenue, and the uncertainty of the Company’s ability to continue as a going concern), included in this Annual Report on Form 10-K for the year ended December 31, 2018.

/s/ Mayer Hoffman McCann P.C.

San Diego, California

March 28, 2019