The catalytic reduction of N2 to NH3 under mild condition remains as a challenging and important chemical process. By performing first-principle density functional theory calculations, the fixation and catalytic reduction of N2 are investigated over a single Co atom supported defective N-doped graphene (Co/N3-Gr) for the first time. All the distal, alternating and enzymatic mechanisms are investigated for the N2 activation and its conversion to ammonia. Our findings reveal that Co/N3-Gr exhibits high catalytic performance for the low-temperature electrochemical reduction of N2 through the enzymatic mechanism. According to our results, the hydrogen evaluation reaction cannot proceed in parallel with the N2 reduction, due to its relatively large over potential (ƞ).