Metal-water primary batteries hold promise for distributed hydrogen production but suffer from limited renewability of metal electrodes in aqueous electrolytes. Here, we introduce a novel concept of a rechargeable zinc-water battery featuring a reversible zinc anode paired with a bifunctional water electrolysis electrode, realized in a specially designed aqueous electrolyte-a mild zinc triflate aqueous electrolyte with the addition of ethylenediaminetetraacetic acid disodium (EDTANa2). The system enables high-purity hydrogen production during discharge and high-purity oxygen production during charge in a membrane-free setup. In the zinc-water battery, EDTANa2 enhances the water-splitting electrode's performance by replacing hydrophobic OTF- anions, ensuring optimal water activity. Additionally, EDTANa2 enhances Zn electrode reversibility by chelating Zn2+, preventing solvated water decomposition during zinc deposition. This integrated battery continuously undergoes charge-discharge cycles for over 55 h at a current density of 6 mA cm-2. Moreover, it achieves a high hydrogen evolution rate of 12.5 mL cm-2 h-1, enabling cost-effective, high-purity hydrogen production without expensive membranes. These findings open new avenues for sustainable hydrogen generation and energy storage in nano energy systems.