Developing cost-effective, efficient bifunctional electrocatalysts for the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) is the heart of metal-air batteries as a renewable-energy technology. Herein, well-distributed nanopolyhedron (NP) CoO grown on iron (Fe) encapsulated in graphitic layers on a nitrogenated, porous two-dimensional (2D) structure, namely, a CN matrix, (NP CoO/Fe@CN), presents an outstanding bifunctional catalytic activity with a comparable overpotential and Tafel slope to those of benchmark Pt/C and IrO. The rationally designed atomic configuration of CoO on the CN matrix has a well-controlled NP morphology with a (111) plane, leading to bifunctional activities for the ORR and OER. Interestingly, the specific interaction between the NP CoO nanoparticles and the CN matrix introduces synergistic coupling and changes the electronic configuration of Co atoms and the CN framework. Benefiting from the synergistic coupling of CoO with the CN matrix, the NP CoO/Fe@CN electrocatalyst exhibits exceptionally high stability and an even lower charge-discharge overpotential gap of 0.85 V at 15 mA cm than that of the Pt/C+IrO catalyst (1.01 V) in Zn-air batteries. This work provides insights into the rational design of a metal oxide on a CN matrix for bifunctional, low-cost electrochemical catalysts.