Exploring efficient bifunctional oxygen electrocatalysts is beneficial to promote the practical applications for rechargeable Zn-air batteries. Herein, a high-efficiency one-pot method is developed to synthesize porous carbon with N, S doping and embedded hollow cobalt oxide nanoparticles. The coordination of polyethyleneimine molecules with cobalt ions enables the formation of organic-inorganic precursors via the co-precipitation with lignosulfonate because of the electrostatic interaction. Under thermal treatment, the hollow cobalt oxide nanoparticles can be well dispersed among the carbon matrix codoped with N, S. The as-prepared composite catalysts exhibit efficient bifunctional activity for electrochemical reduction and evolution reactions of oxygen, thanks to the N, S codoping nature and the hollow cobalt oxide with abundant oxygen vacancies. The bifunctional catalytic activity renders the assembly of high-performance Zn-air battery in an aqueous electrolyte with a specific capacity of 745 mA h gZn-1 and good cycling stability for over 100 h. More importantly, the all-solid-state Zn-air battery is assembled with a polymer-based electrolyte, also exhibiting good cycling stability and flexibility under various bending status.