In recent years, supercapacitors and alkaline Ni–Zn batteries have attracted increasing attention owing to the advantages of high energy density, excellent rate performance, low price, environmental protection and safety. In this study, a ZnCoNi-MOF precursor was prepared on nickel foam (NF) by the solvothermal method, and then a robust transition metal oxide ZnCo₂O₄–NiO nanosheet array material was formed by calcination. As a supercapacitor cathode material, the self-supported ZnCo₂O₄–NiO nanosheet array electrode exhibits a high mass-specific capacitance of 196.67 mA h g⁻¹ (1573.66 F g⁻¹) at a current density of 1 A g⁻¹; even when the current density is increased by 20 times, the electrode still maintains 75.5% of the initial capacity. In addition, the electrode exhibits an excellent performance rate, and the retention rate can still maintain 69.6% of the initial capacity after 10 000 cycles, which indicates that the electrode material has excellent electrochemical performance and cycle stability. When a ZnCo₂O₄–NiO//Zn battery was assembled, the potential platform was impressively extended to 1.70 V. The ZnCo₂O₄–NiO//Zn battery delivers a high capacity of 191.67 mA h g⁻¹ at 1 A g⁻¹. After 6000 cycles at a high current density of 8 A g⁻¹, the capacity retention rate is 63.33%, which is promising for constructing an alkaline Ni–Zn battery with a long life span.