To achieve wearable application, developing highly active and low cost non-precious metal bifunctional oxygen catalysts for foldable solid-state Zn-air battery is still a great challenge. Herein, we report a single-atom cobalt electrocatalyst with CoN4 moieties dispersed on nitrogen-doped graphitic nanosheet (marked as CoN4/NG) by a surfactant-assisted approach. The CoN4/NG catalyst exhibits excellent electrocatalytic activities with a half-wave potential of 0.87 V (versus RHE) for ORR and a low overpotential of 0.38 V at 10 mA cm−2 for OER. Moreover, the liquid Zn-air battery with the CoN4/NG catalyst as the air electrode displays a superior discharging and charging performance, larger power density, higher energy density and robust stability (without any decay after 100 h cycle test), compared to the 20% Pt/C + IrO2 counterpart. Importantly, the CoN4/NG-based flexible solid-state Zn-air battery also exhibits a high power density and a long-term stability of 30 cycles under flat and folded states, which means that the single-atom cobalt catalyst may be a promising candidate for practical applications in wearable flexible solid batteries. Display omitted •We propose a surfactant-assisted approach to synthesize single-atom cobalt catalyst CoN4/NG.•The CoN4/NG catalysts shows excellent electrocatalytic activities for both ORR and OER.•Both the CoN4/NG-based liquid and solid Zn-air batteries exhibit a high power density and a long-term stability.