A non-noble-metal bifunctional catalyst with efficient and durable activity towards both the oxygen reduction reaction (ORR) and the oxygen evolution reaction (OER) is crucial to the development of rechargeable Zn-air batteries. Herein, a facile one-step hydrothermal method is reported for the synthesis of a high-performance bifunctional oxygen electrocatalyst, cobalt-doped Mn3O4 nanocrystals supported on graphene nanosheets (Co–Mn3O4/G). Compare to pristine Mn3O4, this Co–Mn3O4/G exhibits greatly enhanced electrocatalytic activity, delivering a half-wave potential of 0.866 V for the ORR and a low overpotential of 275 mV at 10 mA cm−2 for the OER. The zinc-air battery built with Co–Mn3O4/G shows a reduced charge–discharge voltage of 0.91 V at 10 mA cm−2, an power density of 115.24 mW cm−2 and excellent stability without any degradation after 945 cycles (315 h), outperforming the state-of-the-art Pt/C–Ir/C catalyst-based device.