Recently, two-dimensional transition metal (TM) single atom catalysts (SACs) for metal-air batteries have received tremendous attention attributed to the low cost, high specific surface area, unique chemical and physical characteristics , such as transition-metal disulfide dichalcogenides , two-dimensional (2D) metal-organic frameworks , etc. And intensive efforts have been made to explore/improve their ORR or OER activity and inspiring achievements have been made in recent years . For instance, Li and colleagues demonstrated the Cu-doped MoS2 exhibits the best ORR performance by theoretical screening the TM doped-MoS2 surfaces. Deng et al. comprehensive studied the catalytic activity of 2D transition metal based tetracyanoquinodimethane (TM-TCNQ) monolayers and indicated that the OER activity of Ni-TCNQ is better than Fe-TCNQ, which is regarded as the most promising candidate. Also, as the most popular carbon-based 2D materials, graphene, has shown desired bifunctional catalytic activity for both ORR and OER when a TM atom was loaded on the surface . Specifically, TM-N-C systems derived from graphene have been designed theoretically and experimentally to be one of the most favorable catalytic materials, the single TM atom coordinated with N atoms is regarded as the active center and promotes the high catalytic activity . For the theoretical researches of TM-N-C system, the first principle based on the density functional theory (DFT) is typically adopted to screen and explore the materials with high catalytic performance . For example, simulations indicated CoN4-gra system has been developed to have a stronger active with the overpotential of 0.69, 0.47 eV for ORE and ORR than CoNX-gra (x=1-3) systems, exhibiting the comparably activity with the noble metal catalysts . The FeN4-gra also shows more promising ORR activity than FeNX-gra systems . Lu et al. theoretically proposed the MnN4-gra system and suggested its ORR activity is prior than FeN4-gra.