In order to efficiently evaluate the tunnel face stability in weak surrounding rock, a three-dimensional lower bound finite element limit analysis method (3D LB-FELA) based on second-order cone programming (SOCP) and mesh adaptive refinement strategy for tunnel face stability was proposed. Then, the presented method was used to explore the differences between the Drucker-Prager (D-P) criterion and Mohr-Coulomb (M-C) criterion in the tunnel face stability analysis. First, by transforming the three-dimensional D-P criterion into SOCP constraints, the approximate treatment of yield criteria was avoided, and then the LB-FELA calculation model could be transformed into an efficient SOCP model. Then, a mesh adaptive refinement strategy based on element stress was proposed, which achieved refined simulation of the failure area through smaller scale mesh refinement. Finally, the proposed method was used to study the tunnel face stability, the influence of the series of D-P criteria on the tunnel face stability was thoroughly studied, and the differences between D-P criteria and the M-C criterion were explored. The research results indicate that the 3D LB-FELA based on SOCP technology has high computational efficiency. D-P inscribed circle criterion can better evaluate the tunnel face stability under the limit state. The research results can provide theoretical reference for tunnel face stability research and engineering practice.