Rechargeable zinc-air batteries (ZABs) are a promising energy conversion device, which rely critically on electrocatalysts to accelerate their rate-determining reactions such as oxygen reduction (ORR) and oxygen evolution reactions (OER). Herein, we fabricate a range of bifunctional M–N–C (metal-nitrogen-carbon) catalysts containing M–Nx coordination sites and M/MxC nanoparticles (M = Co, Fe, and Cu) using a new class of γ-cyclodextrin (CD) based metal–organic framework as the precursor. With the two types of active sites interacting with each other in the catalysts, the obtained Fe@C-FeNC and Co@C-CoNC display superior alkaline ORR activity in terms of low half-wave (E1/2) potential (~ 0.917 and 0.906 V, respectively), which are higher than Cu@C-CuNC (~ 0.829 V) and the commercial Pt/C (~ 0.861 V). As a bifunctional electrocatalyst, the Co@C-CoNC exhibits the best performance, showing a bifunctional ORR/OER overpotential (ΔE) of ~ 0.732 V, which is much lower than that of Fe@C-FeNC (~ 0.831 V) and Cu@C-CuNC (~ 1.411 V), as well as most of the robust bifunctional electrocatalysts reported to date. Synchrotron X-ray absorption spectroscopy and density functional theory simulations reveal that the strong electronic correlation between metallic Co nanoparticles and the atomic Co-N4 sites in the Co@C-CoNC catalyst can increase the d-electron density near the Fermi level and thus effectively optimize the adsorption/desorption of intermediates in ORR/OER, resulting in an enhanced bifunctional electrocatalytic performance. The Co@C-CoNC-based rechargeable ZAB exhibited a maximum power density of 162.80 mW cm−2 at 270.30 mA cm−2, higher than the combination of commercial Pt/C + RuO2 (~ 158.90 mW cm−2 at 265.80 mA cm−2) catalysts. During the galvanostatic discharge at 10 mA cm−2, the ZAB delivered an almost stable discharge voltage of 1.2 V for ~ 140 h, signifying the virtue of excellent bifunctional ORR/OER electrocatalytic activity.