Developing the cost-effective or even bifunctional electrocatalysts for both oxygen evolution reaction (OER) and oxygen reduction reaction (ORR) with industrially relevant activity is highly desired for metal-air batteries at the current stage. Herein, in this work, the catalytic performances of the single transition metal (TM) atom embeds graphene sheet with the tetra-coordinates Phosphorus (TMP4) for ORR and OER were investigated based on the density functional theory method. The results demonstrate that the most promising ORR and OER catalytic activity can achieved on the CoP4 with the smallest potential gap ∆E and the lowest overpotentials of 0.37 and 0.32 eV among all TMP4 systems, respectively, and the catalytic activity is even better than that of the traditional Pt and IrO2 catalysts. Furthermore, the AIMD calculation was conducted to confirm the thermodynamics stability of CoP4. This work screens out promising candidates for novel graphene-based bifunctional ORR and OER catalysts and provides the theoretical guidance for the development of single-atom catalysts.