The rational design of bifunctional catalysts for oxygen reduction reaction (ORR)/oxygen evolution reaction (OER) in alkaline electrolyte is of great significance for zinc-air batteries (ZABs). In this study, different types of Fe/Co compounds and nitrogen-doped carbon-based composite catalysts from trimetallic zeolitic-imidazole-framework-derived (ZnFeCo-ZIF) were synthesized by adjusting the ratio of Zn/Fe/Co. Among them, the synthesized CoFe/CoFe2O4-N-doped carbon nanotubes (CoFe/CoFe2O4@NCNTs) have abundant Fe-Nx and Co-Nx activity sites, heterostructures and oxygen vacancies. The experimental results reveal that the electrons of CoFe are transferred to CoFe2O4 at the interface of CoFe/CoFe2O4, which not only enhances the electron transfer ability, but also induces oxygen vacancies to improve the adsorption/desorption capacity of O2 and intermediates. Meanwhile, metal atoms are uniformly dispersed in the N-doped carbon nanotubes to form metal–N sites with high catalytic activity. Therefore, the CoFe/CoFe2O4@NCNTs exhibit excellent electrocatalytic performance, possessing a half-wave potential (E1/2) of 0.878 V and a prominent limiting-current densities (JL) of 6.281 mA cm−2 for ORR, and a low overpotential of 344 mV at 10 mA cm−2 for OER. In particular, the CoFe/CoFe2O4@NCNTs-equiped ZAB possesses a higher open-circuit voltage (1.50 V), a greater maximum power density (193.42 mW cm−2) and a longer cycling performance (160 h). The density functional theory (DFT) calculations show that the CoFe/CoFe2O4 heterostructure can induce the rapid transfer of electrons at the CoFe/CoFe2O4 interface, which promotes the change of the surface electronic structure of the catalyst, and thus helps to enhance the ability of the catalyst to transfer electrons.