Dual-metal single-atom catalysts (DACs) with an intrinsic synergy and multiple coordination structures are flourishing for oxygen reduction reaction (ORR), on the basis of optimization and regulation of the electron configuration for active centers. Herein, a two-step strategy consisting of cavity confinement and post-adsorption is developed to prepare a nitrogen-doped carbon catalyst co-supported by high-density ZnN4 and CoN4 sites (denoted as ZnCo-NC-II) through metal-organic framework (MOF) engineering. Structural characterization incorporated with density functional theory (DFT) calculation demonstrates that electrons are transferred from Zn (donors) to nearby Co (acceptors) through the conjugated graphene π-bond. The optimized Co d-band center achieves a moderate adsorption strength between O2 and CoN4 active sites. So, the rate-determining step (RDS) for the *OOH formation is accelerated. Therefore, ZnCo-NC-II exhibits a distinguished ORR activity with a half-wave potential (E1/2) of 0.86 and 0.79 V (vs RHE) in alkaline and acid media, respectively. The zinc-air battery built with the ZnCo-NC-II catalyst shows excellent electrochemical performance for an immediate practical application. Our work is conducive to an atomic-level clarification on both the composition and design and thereof the synergistic catalytic mechanism with dual-metal sites.