Developing high performance, highly stable, and low-cost electrodes for the oxygen evolution reaction (OER) is challenging in water electrolysis technology. However, Ir- and Ru-based OER catalysts with high OER efficiency are difficult to commercialize as precious metal-based catalysts. Therefore, the study of OER catalysts, which are replaced by non-precious metals and have high activity and stability, are necessary. In this study, a copper–cobalt oxide nanosheet (CCO) electrode was synthesized by the electrodeposition of copper–cobalt hydroxide (CCOH) on Ni foam followed by annealing. The CCOH was annealed at various temperatures, and the structure changed to that of CCO at temperatures above 250 °C. In addition, it was observed that the nanosheets agglomerated when annealed at 300 °C. The CCO electrode annealed at 250 °C had a high surface area and efficient electron conduction pathways as a result of the direct growth on the Ni foam. Thus, the prepared CCO electrode exhibited enhanced OER activity (1.6 V at 261 mA/cm2) compared to those of CCOH (1.6 V at 144 mA/cm2), Co3O4 (1.6 V at 39 mA/cm2), and commercial IrO2 (1.6 V at 14 mA/cm2) electrodes. The optimized catalyst also showed high activity and stability under high pH conditions, demonstrating its potential as a low cost, highly efficient OER electrode material.