A Zn–air battery serves as an energy storage solution to address fossil energy and environmental concerns. However, sluggish kinetics in oxygen reduction reactions (ORRs) and oxygen evolution reactions (OERs) demand innovative, cost-effective, and stable bifunctional catalysts to replace precious metal catalysts. In this study, an FeCo-CNTs/KB catalyst was synthesized by pyrolyzing NH2-MIL-101(Fe) coated with glu-Co and conductive carbon (KB). This hierarchical structure comprises carbon nanotubes (CNTs) grafted onto a carbon matrix, housing abundant FeCo nanoparticles within the nanotubes or matrix. KB introduction enhances FeCo nanoparticle dispersion and fosters uniform CNT formation with smaller diameters, thus exposing active sites. Consequently, the FeCo-CNTs/KB catalyst exhibits remarkable bifunctional electrocatalytic activity: an ORR half-wave potential of 0.84 V and an OER overpotential of 0.45 V (10 mA cm−2). Furthermore, the FeCo-CNTs/KB catalyst in a secondary Zn–air battery showcases enduring charge–discharge performance (≥300 h).