A　high　active　and　stable　bifunctional　oxygen　electrocatalyst　of　Co–CoO　multiphase　nanoparticles　(NPs)　encapsulated　in　N,S　co-doped　carbon　shells　(Co–CoO@NSC)　is　designed　and　constructed　by　in-situ　S　doping　of　ZIF-67　with　thiourea　and　subsequent　pyrolysis,　which　not　only　generates　small　Co–CoO　NPs　due　to　the　steric　effect,　but　also　creates　more　active　sites　and　defects.　First-principles　simulations　reveal　that　in-situ　S-doping　optimizes　the　charge　distribution　of　Co–N4　sites　and　Co–O–C　bonds,　which　reduces　the　formation　energy　of　*OOH　and　then　improves　the　ability　of　oxygen　adsorption　and　hydrogen　peroxide　desorption.　The　optimized　Co–CoO@NSC　exhibits　excellent　catalytic　activity　with　the　overpotential　of　only　279　mV　at　10　mA　cm−2　for　OER　and　the　half-wave　potential　of　0.89　V　for　ORR,　outperforming　that　of　most　recent　reported　bifunctional　electrocatalysts.　Our　Co–CoO@NSC　catalyst　indicates　the　ΔE　(ΔE　=　Ej=10　(OER)　−　E1/2　(ORR))　of　0.68　V,　which　is　smaller　than　the　Pt/C　+　RuO2　system.　Flexible　solid-state　Zn-air　battery　with　Co–CoO@NSC-5　as　air-electrode　possesses　a　high　power　density　(87.7　mW　cm−2)　as　well　as　good　bending　flexibility.　The　simple　synthesis　method　proposed　in　our　paper　is　beneficial　for　inspiring　the　development　for　high　active　and　stable　bifunctional　non-noble　metal　electrocatalysts　in　next-generation　flexible　electronic　devices.　©　2020　Elsevier　B.V.