Electrochemical N-2 reduction under mild conditions has been regarded as a promising alternative to the conventional Haber-Bosch process. In the electrochemical reaction, a highly efficient catalyst plays an important role. Herein, we studied a series of bimetallic atoms catalysts, namely, two transition metal atoms doped on the PC6 monolayer (TM2@PC6, TM = Cr, Mn, Fe, Co. Ni, Mo, Ru, Rh, W, and Ir), to examine the electrocatalytic performance for nitrogen reduction reaction by employing the density functional theory computations. Co-2@PC6 is screened out to be the best candidate for the N-2 reduction, which has high Faradaic efficiency and lowest limiting potential of -0.28 V, followed by Mo-2@PC6, and Fe-2@PC6 with limiting potentials of -0.46, and -0.50 V, respectively. These predicted candidates have comparable or even better NRR catalytic activity than the other common two-dimensional materials. The N2H* formation is the potential-determining step for these catalysts. N-2 with side-on adsorption configuration (occurred only for Co-2@PC6) has the best NRR performance. This work not only provides the potential NRR catalyst but also gives insight into the mechanism to advance the development of efficient NRR catalysts.