The explorations of efficient electrocatalysts to accelerate oxygen reactions in a wide temperature range is a crucial issue to the development of zinc-air batteries (ZAB) for all-climate applications. Herein, the Co-CoSe heterogeneous furry fibers (Co-CoSe@NHF) are developed as a bifunctional oxygen electrocatalyst for ZAB towards wide-temperature range applications. The Co-CoSe heterostructure with large work function difference (ΔWF) endows interfacial electron redistribution, which builds strong interfacial built-in electric field (BIEF) and improves the oxygen reactions. Meanwhile, the Co-CoSe heterostructure is encapsulated by in-situ grown carbon nanotubes, and forms the hollow fiber (NHF) with furry surface and beads-on-string configuration. The highly porous and conductive NHF configuration facilitates the fast kinetics and favors to accommodates volume change during cycling. As a result, the Co-CoSe@NHF achieves the superior bifunctional properties and good reliability for oxygen reactions. Integrated with the Co-CoSe@NHF fiber, the ZAB cell delivers the superior power density (301 mW cm−2) and long-term cycling stability over 280 h at 25 °C, and maintains the power densities of 126 mW cm−2 even the temperature decreases to −25 °C. Moreover, the solid-state ZAB exhibits significant flexibility and superior properties in a wide temperature range. Therefore, this work not only proposes a new strategy to design the high-performance bifunctional electrocatalysts, but also propels the development of flexible power sources for all-climate applications.