Developing transition-metal based bifunctional electrocatalysts to efficiently drive oxygen evolution reaction and oxygen reduction reaction is an urgent demand for the implementation of rechargeable Zn-air batteries. Transition-metal sulfides are emerging as alternatives to precious metal-based electrocatalysts, however, their bifunctional activities are usually restricted by inferior electrical conductivities and limited electrochemical active sites. Herein, we highlight a novel metal-organic frameworks derived nitrogen-doped carbon nanofiber coupled FeS2–CoS2 (FeS2–CoS2/NCFs) by a combination of electrospinning and atomic-layer-deposition approach. Benefiting from the large exposed surface active sites of hierarchical structure and the abundant interfacial vacancies in FeS2–CoS2 heterointerface, the FeS2–CoS2/NCFs integrated electrocatalyst delivers a high bifunctional activity together with a good durability in alkaline medium. Notably, the liquid Zn-air battery assembled with this FeS2–CoS2/NCFs electrode displays a considerable peak power density of 257 mW cm−2, a high specific capacity of 814 mA h g−1 and a long cycling life of 250 h, superior to precious metal based Zn-air batteries. Moreover, the flexible solid-state Zn-air battery using such FeS2–CoS2/NCFs electrode can stably power LED panels even under twisting state, demonstrating practical potentials in wearable and portable electrochemical devices.