Covalent organic framework (COF) is a promising material for oxygen catalysis. Herein, a novel highly stable conjugated two-dimensional Poly (benzimidazole porphyrin-cobalt) (PBIPorCo) with a large delocalization energy is synthesized by meso-5, 10, 15, 20-tetra (4-cyano-phenylporphyrin) cobalt (TCNPorCo) and 3,3′-diaminobenzidine (DAB). The decrease in energy between the HOMO and LUMO orbitals of PBIPorCo could enhances the capability of electrons gain-lose during the catalytic process. Nitrogen-rich environment benzimidazole (BI) group can transfer electrons to the Co-N4 site and enhance the protonation process in the oxygen reduction reaction (ORR). The π-π interactions between PBIPorCo and three-dimensional graphene (3D-G) which form “electron donor-π-electron acceptor” structure to boost the bifunctional oxygen catalysis process. PBIPorCo/3D-G exhibits outstanding bifunctional oxygen catalytic performance (ΔE=0.62 V) and the outstanding performance for zinc-air batteries. It indicates satisfactory potential application in fuel cells (FC) and overall water splitting (OWS). This work presents a promising strategy for the design of novel COF as bifunctional oxygen catalysts.