The development of battery-type electrode materials with hierarchical nanostructures has recently gained considerable attention in high-rate hybrid supercapacitors. For the first time, in the present study novel hierarchical CuMn2O4 nanosheet arrays (NSAs) nanostructures are developed using a one-step hydrothermal route on a nickel foam substrate and utilized as an enhanced battery-type electrode material for supercapacitors without the need of binders or conducting polymer additives. X-ray diffraction, scanning electron microscopy (SEM), and transmission electron microscopy (TEM) techniques are used to study the phase, structural, and morphological characteristics of the CuMn2O4 electrode. SEM and TEM studies show that CuMn2O4 exhibits a nanosheet array morphology. According to the electrochemical data, CuMn2O4 NSAs give a Faradic battery-type redox activity that differs from the behavior of carbon-related materials (such as activated carbon, reduced graphene oxide, graphene, etc.). The battery-type CuMn2O4 NSAs electrode showed an excellent specific capacity of 125.56 mA h g−1 at 1 A g−1 with a remarkable rate capability of 84.1%, superb cycling stability of 92.15% over 5000 cycles, good mechanical stability and flexibility, and low internal resistance at the interface of electrode and electrolyte. Due to their excellent electrochemical properties, high-performance CuMn2O4 NSAs-like structures are prospective battery-type electrodes for high-rate supercapacitors.