Highly efficient and flexible air-electrodes play a vital role in the development of solid-state metal-air batteries for wearable electronic devices. However, the practical application of air-electrodes is impeded by the multistep synthesis and poor flexibility. Herein, metal/nitrogen co-doped carbon nanofiber membranes are synthesized by integrated core-shell electrospun, in which Co-N sites are atomically dispersed in the porous shell and specific carbon nanofibers with super-flexibility form backbones in the core. Owing to a high specific surface area, a 3D porous network structure and atomically dispersed Co-N active sites, as-prepared membranes demonstrate a remarkable bifunctional electrocatalytic performance towards oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) with a low potential gap of 0.719 V. Furthermore, the flexible Zn–air battery featuring a freestanding air-electrode by as-fabricated membranes displays an outstanding open-circuit voltage (1.461 V), a high peak power density (60.3 mW cm) and an ultra-narrow and stable discharge-charge voltage gap of 0.61 V under different bending angles, which are among the best values reported for self-supported flexible Zn-air batteries. This work paves a new way to prepare integrated freestanding air-electrodes as power sources for flexible electronic devices.