Zinc-based batteries have attracted attention for their safety in aqueous electrolytes with low cost, environmental friendliness, and high capacity. In this study, layered double hydroxide, a solid-state OH− ion conductor, was hybridized with sodium polyacrylate hydrogel to construct a strong elastic hydrogel electrolyte (PANa-LDH) with high OH− ion conductivity. PANa-LDH, KOH was introduced by dipping into 6.0 M KOH solution, showed a significantly high ionic conductivity of 0.213 S cm−1 at 30 °C. A solid-state battery was fabricated using nickel-cobalt hydroxide cathode, PANa-LDH electrolyte, and zinc anode. The high specific capacity of 287 mAh g−1 was obtained at 0.1 A g−1 with high energy and power densities of 212 Wh kg−1 and 73 kW kg−1 (based on the cathode weight), respectively.