The failure criterion of rocks is a critical factor involved in reliability design and stability analysis of geotechnical engineering. In order to accurately evaluate the triaxial compressive strength of rocks under different confining pressures, a nonlinear empirical strength criterion based on Mohr-Coulomb criterion was proposed in this paper. Through the analysis of triaxial test strength of 11 types of rock materials, the feasibility and validity of proposed criterion was discussed. For a further verification, six typical strength criteria were selected, and the prediction results of each criterion and test results were statistically analyzed. The comparative comparison results show that the prediction results obtained by applying this new criterion to 97 conventional triaxial compression tests of 11 different rock materials are highly consistent with the experimental data. Statistical analysis was executed to assess the application of the new criterion and other classical criteria in predicting the failure behavior of rock. This proposed empirical criterion provides a new reference and method for the determination of triaxial compressive strength of rock materials.