In this paper, both primary and rechargeable Zn–air batteries are constructed using La2O3/Co3O4/MnO2–CNTs hybrid nanocomposites as air electrodes for high-performance energy storage and conversion. The air electrode hybrid catalysts with controlled morphology are prepared by a facile hydrothermal self-assembly process, which exhibits highly bi-functional catalytic activity for both the oxygen reduction reaction (ORR) and the oxygen evolution reaction (OER) during discharge and charge processes in a rechargeable Zn–air battery. When these catalysts are integrated into a practical primary Zn–air battery, a high open circuit voltage of 1.5V is achieved along with a high discharge peak power density of 295mWcm−2. The specific capacity normalized to the mass of consumed Zn is 821mAhg−1, corresponding to a high energy density of 970Whkg−1, which shows this zinc–air battery’s performance is higher than any battery currently commercially available to meet the requirements of high-power electric equipment. More specifically, the electrochemically rechargeable Zn–air battery incorporating by this bifunctional catalyst exhibits an unprecedented small charge–discharge voltage polarization, high reversibility and high stability, suggesting this battery can be used as a power source for portable electronics, armamentarium and electrical vehicles. Furthermore, a flexible, rechargeable Zn–air battery as a wholly solid-state energy storage device, and exhibiting good peak power density and decent stability, should be viable in other practical applications such as smart electronics and wearable electronic devices.