The oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) are considered to be the most important processes in metal-air batteries and regenerative fuel cell devices. Metal-organic polymers are attracting interest as promising precursors of advanced metal/carbon electrocatalysts because of their hierarchical porous structure along with the integrated metal-carbon framework. We developed carbon-coated CNTs with Ni/Fe and Cu/Fe as active sites. Experimental observations from X-ray photoelectron spectroscopy and X-ray absorption analysis suggest that C@CNT[Ni] outperforms C@CNT[Cu] in the ORR and OER, which is further supported by density functional theory calculations. C@CNT[Ni] exhibits a higher onset potential (0.99 V vs RHE) and a smaller Tafel slope (40.2 mV decade-1) compared to those of C@CNT/[Cu] in an alkaline electrolyte (0.94 V vs RHE and 46.5 mV decade-1, respectively). Such circumstances are attributed to the alloying effect between Ni and Fe in C@CNT[Ni], in contrast to the existing copper iron oxide phase in C@CNT/[Cu]. It is noteworthy that C@CNT[Ni] also displayed an improved OER, demanding its bifunctional property. As a proof of concept, C@CNT[Ni] was utilized in zinc-air batteries, which shows a high energy efficiency of ∼60%, a small charge-discharge voltage gap of 0.78 V, and excellent cycling performance (∼120 h) at 5 mA cm-2 and 25 °C. This protocol expands the utility of novel metal-organic hyper-cross-linked polymer-derived bimetallic electrocatalysts for clean energy research.