The demand for electrochemical energy storage (ESS) systems and their market size has drastically increased in many applications ranging from portable devices through electric vehicles to large-scale grid systems over the past decades. Yet, a more advanced ESS is required due to the safety issues and limited energy density of currently commercialized lithium-ion batteries (LIBs) for wide and matured applications. As a solution to this challenge, zinc-air batteries (ZABs) have gained tremendous attention due to their high energy density, low cost, environmental friendliness, and much lower fire risk characteristics. ZABs utilize oxygen from the atmosphere at their cathode during discharge, where the atmospheric oxygen is reduced to hydroxide via an oxygen reduction reaction (ORR). On the other hand, hydroxide is released as oxygen via oxygen evolution reaction (OER) during charge. The fact that oxygen is drawn directly from the air enables high gravimetric and volumetric energy densities of ZABs compared to those of commercial LIBs. However, the sluggish kinetics of the four-electron transfer steps in ORR and the mass transport of oxygen in OER remain major challenges for the practical application of ZABs. Meanwhile, precious metal-based catalysts such as Pt/C and RuO2 are known to have good catalytic activity towards ORR and OER. However, the integration of different catalysts into the same cathode is very difficult. Additionally, the high cost and natural scarcity of novel metals limit their usage for practical applications.We synthesized a bifunctional CoO/Mn3O4 heterostructure (CMH) OER/ORR electrocatalyst which was derived from metal-organic framework (MOF) for excellent activities in ZABs. The CMH cathode exhibited high ORR and OER performances, as demonstrated by the higher ORR current density than that of the Pt/C catalyst as well as the low OER overpotential exceeding those of the RuO2 catalyst. Remarkably, atomic structures of the CMH were elucidated using global optimization of genetic algorithm integrated with the machine learning force field. By adopting first-principles electronic structure calculations, we further revealed the charge transfer and active sites for both reactions in the identified heterojunction. Furthermore, assembling CMH cathode and Zn metal anode into a ZAB full-cell configuration achieves a ~5.5-fold higher energy density of 879 Wh kg-1 exceeding those of commercial lithium-ion batteries (LIBs), a high-discharge outstanding power density that is 1.39 times higher than novel metal catalysts, and robust cycle stability with negligible voltage decay which is far superior to that of benchmark Pt/C+RuO2 electrocatalysts.