▎ 摘　　要

The high-dense metal-air batteries are difficult to commercialize on a large scale mainly because of sluggish kinetics of air electrode. The catalysts are of crucial importance for the rate of oxygen reduction reaction (ORR), among which Pt-based catalysts for ORR have shortcomings in stability and cost, and the kind of catalysts with adding C and N to transition metals receive more attention. Here we analyze catalytic performance of graphene supported transition metals-N-4(M-N-4@G) for ORR based on density functional theory (DFT), verifying rationality of such catalysts with five different transition metals (Pt, Fe, Co, Pd and Ni) embedded in the graphene, and demonstrating that Fe-N-4@G has better ORR performance than Pt-N-4@G. Moreover, a proposed mechanism of ORR (generating free *O and *OH) is explored to optimize ORR by means of transition-state search in the DFT calculation. Additionally, a novel phenomenon is observed that graphene has a strong attraction to hydrogen atoms, which is facilitated to promote hydrogen evolution reaction of graphene supported catalysts.