Designing bifunctional oxygen electrocatalysts with high activity, lasting stability, and low-cost for rechargeable zinc-air batteries (RZABs) is a tough challenge. Herein, an advanced electrocatalyst is prepared by anchoring atomically dispersed Co atoms on N-doped graphene-like hierarchically porous carbon nanosheets (SA-Co-N₄-GCs) and thereby forming Co-N₄-C architecture. Its unique structure with excellent conductivity, large surface area, and three dimensional (3D) interconnected hierarchically porous architecture exposes not only more Co-N₄ active sites to accelerate the kinetics of both oxygen reduction reaction (ORR) and oxygen evolution reaction (OER), but also provides an efficient charge/mass transport environment to reduce diffusion barrier. Consequently, SA-Co-N₄-GCs exhibits excellent ORR/OER bifunctional activities and durability, surpassing noble-metal catalysts. Liquid RZABs using SA-Co-N₄-GCs cathodes display a high open-circuit voltage of 1.51 V, a remarkable power density of 149.3 mW·cm⁻², as well as excellent stability and rechargeability with faint increase in polarization even at a large depth of charge–discharge cycle with 16 h per cycle over an entire 600 h long-term test. Moreover, flexible quasi-solid-state RZABs with SA-Co-N₄-GCs cathodes also deliver a considerable power density of 124.5 mW·cm⁻², which is even higher than that of liquid batteries using noble-metal catalysts. This work has thrown new insight into development of high-performance and low-cost electrocatalysts for energy conversion and storage.