The development of highly efficient and earth-abundant oxygen evolution/reduction reaction (OER/ORR) catalysts is essential for rechargeable metal–air batteries. Herein, cobalt-based hydroxide nanoparticles @ N-doping carbonic framework (CoOHCat@NCF) core–shell structures have been designed as highly stable and efficient OER/ORR bifunctional catalysts. The obtained composite shows enhanced catalytic activities and excellent stability in alkaline media. In the OER, a high turnover frequency (2.03 s^–1 at an overpotential of 0.36 V), low overpotential at high current density (100 mA·cm^–2 requiring an overpotential of 0.38 V), and excellent stability (100 mA·cm^–2 for one week with no activity loss) have been achieved. Furthermore, although cobalt species-based catalysts are known as good ORR catalysts, their hybridization with NCF obtained from metal organic frameworks successfully enhanced their ORR activities. The efficient activity of CoOHCat@NCF as a bifunctional oxygen electrocatalyst can be ascribed to the core–shell structures stabilizing the active catalytic sites and the porous shell structure favoring electrocatalysis-related mass transport.