Carbon materials featuring hierarchical pores and atomically dispersed metal sites are promising catalysts for energy storage and conversion applications. Herein, we developed a facile strategy to construct functional carbon materials with a fluffy peony-like structure and dense binary FeCo-Nx active sites (termed as f-FeCo-CNT). By regulating the metal content in precursors, a 3D interconnected conductive carbon nanotubes network was in-situ formed throughout the atomically dispersed FeCo-NC matrix during pyrolysis. Taking advantage of rich pore hierarchy and co-existence of highly active FeCo-Nx sites and beneficial FeCo alloy nanoparticles, the f-FeCo-CNT material exhibited excellent bifunctional performance towards oxygen reduction/evolution reactions (ORR/OER) with respect to the atomically dispersed FeCo-NC (SA-f-FeCo-NC) and commercial Pt/C+RuO2 mixture, surpassing the SA-f-FeCo-NC with a 20 mV higher ORR half-wave potential and a 100 mV lower OER overpotential (at 10.0 mA cm-2). Remarkably, the f-FeCo-CNT-assembled Zn-air battery (ZAB) possessed a maximum specific power of 195.8 mW cm-2, excellent rate capability, and very good cycling stability at large current density of 20.0 mA cm-2. This work provides a facile and feasible synthetic strategy of constructing low-cost cathode materials with excellent comprehensive ZAB performance.