High-entropy materials have attracted extensive attention as emerging electrode materials in various energy applications due to their flexible tunability, unusual outstanding activities, and cost-effectiveness using multiple earth-abundant elements. We introduce a novel high-entropy composite oxide with the five elements of Cu, Ni, Co, Fe, and Cr (HEO-3CNF) for use in the oxygen evolution reaction (OER) in electrocatalytic water splitting. HEO-3CNF is composed of two phases with a non-equimolar, deficient high-entropy spinel oxide of (Cu0.2−xNi0.2Co0.2Fe0.2Cr0.2)3O4 and monoclinic copper oxide (CuO). Electrochemical impedance spectroscopy (EIS) with distribution of relaxation times (DRT) analysis validates that the HEO-3CNF-based electrode exhibits faster charge transfer than benchmark CuO. It results in improved OER performance with a lower overpotential at 10 mA/cm2 and a Tafel slope than CuO (518.1 mV and 119.7 mV/dec versus 615.9 mV and 131.7 mV/dec, respectively) in alkaline conditions. This work may provide a general strategy for preparing novel, cost-effective, high-entropy electrodes for water splitting.