The rational design and preparation of promising cathode electrocatalysts with excellent activity and strong stability for metal-air batteries is a huge challenge. In this work, we innovate an approach of combining solvothermal with high-temperature pyrolysis utilizing zeolitic imidazolate framework (ZIF)-8 and ZIF-67 as the template to synthesize a novel hybrid material of hierarchical porous yolk–shell Co-N-C polyhedron nanocatalysts engaged in graphene nanopocket (yolk–shell Co-N-C@GNP). The obtained catalyst exhibits prominent bifunctional electrocatalytic performance for oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) in the alkaline condition, in which the half-wave potential is 0.86 V for ORR, and the over-potential for OER is 0.42 V at 10 mA·cm⁻². The rechargeable aqueous Zn-air battery fabricated with yolk–shell Co-N-C@GNP cathode deliveries an open circuit voltage (OCV) of 1.60 V, a peak power density of 236.2 mW·cm⁻², and excellent cycling stability over 94 h at 5 mA·cm⁻². The quasi-solid-state Zn-air battery (ZAB) using yolk–shell Co-N-C@GNP displays a high OCV of 1.40 V and a small voltage gap of 0.88 V in continuous cycling tests at 2 mA·cm⁻². This work provides a valuable thought to focus attention on the design of high-efficient bifunctional catalysts with hierarchical porous yolk–shell framework and high-density metal active sites for metal-air battery technologies.