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• Co 1-x S@NC is prepared via a facile "CBD deposition-PDA coating-sulfurization" method. • The excellent OER and ORR electrocatalytic activities both mainly derive from Co 1-x S. • The 3D array structure of Co 1-x S@NC facilitates OER/ORR-related charge-and-mass transport. • There is wrapping-protection of NC on Co 1-x S and strong electron coupling between them. • Promising quasi-solid-state rechargeable Zn-air battery based on Co 1-x S@NC is achieved. It is of great significance to develop high-performance bifunctional electrocatalysts for catalyzing two vital reactions in rechargeable zinc-air battery (ZAB). Transitional metal sulfides and N-doped carbon materials are widely reported as effective electrocatalysts of oxygen evolution reaction (OER) and oxygen reduction reaction (ORR), respectively. Herein, an 3D-array-structured catalyst composed of Co 1-x S nanoneedles enwrapped by nitrogen-doped carbon (NC) is in-situ grown on carbon fibre paper substrate. It is revealed that the metastable hexagonal Co 1-x S itself possesses attractive electrocatalytic activities toward both OER and ORR. Additionally, owing to the wrapping-protection effect of polydopamine-derived NC on Co 1-x S, the strong electron coupling between Co 1-x S and NC, and the 3D array structure, Co 1-x S@NC presents excellent OER/ORR catalytic activities and long-term stabilities, superior to Co@NC, Co 1-x S, and NC, and comparable to noble metals and other reported state-of-the-art bifunctional oxygen electrocatalysts. A small energy gap (Δ E) of 0.66 V between the ORR half-wave potential (0.86 V vs RHE) and OER potential (1.52 V vs RHE) at a current density of 10 mA cm−2, and a diffusion-limit ORR current density of 11.37 mA cm−2 are achieved. Notably, the flexible ZAB using the catalyst exhibits a markedly higher peak power density of 242 mW cm2, and a small charge/discharge voltage gap of ∼ 0.68 V with a high round-trip efficiency of ∼ 64% when cycling at 5 mA/cm2. [ABSTRACT FROM AUTHOR]