N2 fixation in atmosphere is an important issue in modern chemistry. Designing an ideal electrochemical nitrogen reduction reaction (NRR) catalyst to overcome the sluggish reaction kinetic and ultralow selectivity is still the significant challenge. Herein, we screened the potential catalyst to accelerate N2 fixation by designing the single transition metal (TM) atoms (Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Mo, W, Ru and Rh) supported on the edge of graphene. Our calculations revealed that the Co atom supported on the graphene edge could selectively stabilize *N2H species and destabilize *NH2 species, leading to the highest catalytic activity and selectivity for N2 fixation at the ambient conditions. In addition, the enzymatic mechanism of eNNR have the lowest overpotential of 0.72 V. This theoretical work will give a new perspective to design an available catalyst for NRR. © 2020