Exploiting bifunctional electrocatalysts with excellent activity and stability towards oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) is of great importance for the practical application of rechargeable metal–air batteries. Herein, we report a novel bimetallic-ion co-exchange combined pyrolysis strategy using bio-MOF-1 as the self-template to synthesize NiCo nanoalloy-Co-N4 embedded hierarchical porous carbon (CoNi-CoN4-HPC-900), which endows good electrical conductivity, large surface area and rich highly-dispersed CoNi-CoN4 active sites identified from X-ray absorption spectroscopy, resulting in outstanding electrocatalytic activity for both ORR and OER in alkaline solution. In situ Raman spectroscopy testifys that the electrocatalytic processes occur via the redox of Co(Ni)(II and Ⅲ) species. Density functional theory calculations are performed to study the ORR and OER activity on the CoNi-CoN4 and CoN4 active sites. The CoNi-CoN4-HPC-900 endows a flexible rechargeable Zn-air battery with an open circuit voltage of 1.50 V and a peak power density of 116 mW cm−2, and excellent flexibility and cycling stability as a cathode. This bimetallic-ion-coexchange strategy of MOFs gives an effective methodology involving bimetallic-ion-coexchange strategy to design and prepare bifunctional electroctalysts in metal-air batteries but also brings an intensive insight into ORR and OER fundamentals.