Zn-quinone batteries, with the merit of high reversibility, show great potential in the energy storage and conversion system, but the low working voltage and power density limit their application. We here report a rechargeable asymmetric alkali-acid electrolyte Zn-quinone battery (AAAZQB, 3AZQB) with the Zn anode in alkali and the highly reversible quinone cathode in acid. The elaborate asymmetric alkali-acid electrolyte design, enables the redox of Zn and quinone can act in their optimal conditions, the electrochemical neutralization energy can be harvested simultaneously. As a result, the 3AZQB delivers an open circuit voltage of 1.95 V, a peak power density up to 315 mW cm−2 and a highly strong stability with a reversible charging/discharging voltage gap of 200 mV, which are much better than those of Zn-air batteries and Zn-quinone batteries reported before.