Hydrogen ions (H+) and hydroxide ions (OH-) are regarded as ideal charge carriers for rechargeable batteries thanks to their small size, high ion mobility, low cost, and wide flexibility compared to the metal ions. However, the implementation of storage of both H+ and OH- in one electrochemical energy device face grand challenge due to incompatibility between H+ and OH-. Herein, we report an alkali-acid Zn-MoO3 hybrid battery that employ H+ and OH- as charge carriers of cathode and anode, respectively, in which the insertion/deinsertion of H+ take place on layer structured MoO3 cathode in acid while OH- are involved in alkaline conversion Zn anode, which offers a promising route to well address the incompatible issues of H+ and OH- in one electrolyte. The as-built hybrid battery can deliver a high open-circuit voltage of 1.85 V, a high rate capability, a high capacity of 158 mAh g-1 at a current density of 5 A g-1, and excellent capacity retention of above 90% over 200 cycles. This work sheds light on the development of aqueous energy devices with high voltage and energy density through materials engineering and device optimization.