At present, developing bifunctional electrocatalysts plays an important role in the field of metal-air batteries and fuel cells. Non-noble transition metal single atoms loaded on the nitrogen-doped graphene sheets (M-N-C) are considered to be the most promising materials to replace noble metal electrocatalysts owing to the metal coordination compounds (MNxO4-x) in M-N-C with high catalytic activity. In this work, oxygen atoms were introduced in Fe-N-C to construct FeNxO4-x (x = 0, 1, 2, 3, 4) for studying the effect of coordination number x on the catalytic performance of ORR/OER. It was found that Fe-N-C showed the best thermodynamic stability and catalytic activity when x = 4. In addition, the effect of transition metal type was studied by introducing different transition metals, such as M = Mn, Fe, Co, Ni, Cu, in MN4. Among them, the thermodynamically stable CoN4 structure was the best choice for M-N-C to reach the highest ORR/OER catalytic activity. It is expected that this paper could provide a theoretical reference for adjusting the coordination environment of transition metal single atoms and designing high efficient bifunctional electrocatalysts.