To develop asymmetric Zn-air battery with high voltage and power density, acidic stable bi-functional electrocatalyst for oxygen reduction reaction and oxygen evolution reaction plays an important role. Here, with two-dimensional metal-organic framework as precursor, a Co-Nx based electrocatalyst is synthesized. This electrocatalyst shows flaky shaped appearance. In its framework, Co-Nx and metallic Co particles with the size about 15–20 nm distribute evenly in N-doped mesoporous carbon matrix. In 0.1 M HClO4, its oxygen reduction reaction completes with a four-electron process. The onset and half-wave potentials are 0.86 and 0.82 V, respectively. The oxygen evolution reaction activity of this electrocatalyst is still outstanding. To obtain 10 mA cm−2 current, it merely requires a low overpotential of 328 mV. The electrocatalyst exhibits promising stability in both oxygen reduction reaction and oxygen evolution reaction process. With this electrocatalyst as cathode and Zn plate as anode, an asymmetric Zn-air battery is assembled. The open circuit voltage of this battery achieves 2.16 V with peak power density 300 mW cm−2. When discharge at 20 mA cm−2, its power density arrives at 1189 Wh·kg−1. This asymmetric Zn-air battery also shows attracting cycling stability during charge-discharge process and keeps constant for 15 h.