The large-scale deployment of renewable energy is dependent on the accessibility of cost-effective and long cycle life energy storage solutions. Rechargeable Zn-air batteries are a good candidate, but the aggressiveness of their alkaline electrolyte reduces the battery life. Replacing the alkaline electrolyte with a neutral/quasi-neutral solution is a logical alternative. The energy efficiency of neutral/quasi-neutral Zn-air batteries is however lower than alkaline Zn-air batteries due to the more sluggish kinetics of the oxygen electrochemical reactions in pH-neutral solution. This article describes the development of an efficient hybrid battery design to close the performance gap between alkaline and neutral/quasi-neutral Zn-air batteries. Specifically, a Mn2+-containing electrolyte is used to complement the Zn-air chemistry with a facile MnO2/Mn2+ redox reaction. The quasi-neutral Zn-air battery formulated as such shows a record high round-trip energy efficiency of 63.2% by using only a low-cost phosphated MnO2 oxygen electrocatalyst; which is as energy efficient as the alkaline rechargeable Zn-air batteries but without the cycle life problem of the latter.