This work addresses the challenges faced by oxygen catalysis applications in neutral media, which are hindered by sluggish kinetics and severe carbon corrosion. To overcome these issues, a bifunctional oxygen catalyst (KB@Co-C3N4) was developed by utilizing graphitic carbon nitride (g-C3N4) to support Co-Nx active sites and simultaneously to wrap Ketjen black (KB) to form a wonton structure. The resulting catalyst exhibited excellent ORR/OER activity and good stability in neutral electrolytes. The KB@Co-C3N4 catalyst demonstrated a half-wave potential (E1/2) of 0.723 V and only a 9 mV decay after 40000 cycles of ORR accelerated durability test (ADT). In terms of OER, the overpotential at 10 mA cm−2 (η10) of KB@Co-C3N4 was 550 mV, with negligible increase observed even after 20 k cycles of OER ADT. The zinc-air battery incorporating KB@Co-C3N4 exhibited superior performances over other benchmark bifunctional counterparts in open-circuit voltage (1.52 V), galvanostatic discharge/charge performance and cycling duration (985 h at 5 mA cm−2). The theoretical investigation revealed that the engineered electronic structures of the metal active sites enable precise regulation of the charge distribution of Co centers, leading to optimized adsorption and desorption of oxygenated intermediates. The high stability of the catalyst is attributed to the chemically stable C3N4, which strengthens Co-Nx active sites and protects KB against carbon corrosion by wrapping KB to form the wonton structure.