Efficient and low-cost bifunctional electrocatalysts for the oxygen reduction reaction (ORR) and the oxygen evolution reaction (OER) are of vital importance in energy conversion. Herein, an excellent highly dispersed Co nanoparticle decorated N-doped defective carbon nano-framework (Co-N-C) derived from a ZnCo bimetal organic framework (bi-MOF) is reported. A high specific surface area originating from zinc evaporation facilitates the adsorption and desorption of oxygen, which promotes the accessibility of catalytic sites. The abundant Co-N-C species act as strong bridging bonds between Co nanoparticles and carbon materials which facilitate interfacial electron transfer. Co-N-C-0.5 (0.5 represents the molar ratio of Zn in the initial ZIF-67) exhibits a low overpotential gap of 0.94 V due to the number of active sites (e.g. N-doped defective carbon and the CoNx/Co composite) and fast interfacial electron transfer. In addition, a hybrid Na-air battery with the Co-N-C-0.5 material displays a low voltage gap of 0.31 V and a high round-trip efficiency of 90.0% at a current density of 0.1 mA cm-2. More importantly, the hybrid Na-air battery shows fantastic cyclability for charging and discharging due to its stable structure. Our results confirm Co-N-C materials derived from a bi-MOF as alternatives to high-cost Pt/C catalysts for ORR and OER activities in metal-air batteries.