Developing bifunctional oxygen electrocatalysts with superior catalytic activities of oxygen reduction reaction (ORR) and oxygen revolution reaction (OER) is crucial to their practical energy storage and conversion applications. In this work, we report the fabrication of Co/CoxSy@S,N-codoped porous carbon structures with various morphologies, specific surface areas, and pore structures, derived from controllably grown Co-based metal–organic frameworks with S- and N-containing organic ligands (thiophene-2,5-dicarboxylate, Tdc; and 4,4′-bipyridine, bpy) utilizing solvent effect (e.g., water and methanol) under room temperature and hydrothermal conditions. The results demonstrate that Co/CoxSy@S,N-codoped carbon fibers fabricated at a pyrolytic temperature of 800 °C (Co/CoxSy@SNCF-800) from Co-MOFs fibers fabricated in methanol under hydrothermal conditions as electrocatalysts exhibit superior bifunctional ORR and OER activities in alkaline media, endowing them as air cathodic catalysts in rechargeable zinc–air batteries with high power density and good durability.