A facile and scalable method is developed to synthesize layered CuCo2O4 nanosheets@MnO2 nanoflakes core–shell arrays (CuCo2O4@MnO2 CAs) on Ni foam. Interestingly, the superstructures of the core include well-arranged micrometer length rectangular two-dimensional (2D) nanosheets with high pore volume. Subsequently, MnO2 nanoflakes are vertically grown on the CuCo2O4 nanosheets to form a core–shell architecture. The electrochemical measurements demonstrate a high specific capacitance of 416 F g−1 at a current density of 1 A g−1 with excellent rate capability and remarkable cycling stability (92.1% retention after 4200 cycles). Impressively, the optimized CuCo2O4@MnO2//AG ACS cell can be cycled reversibly in a wide voltage region as high as 2.0 V and exhibits a specific capacitance of 78 F g−1 at a current density of 1 A g−1 with a maximum energy density of 43.3 W h kg−1. These encouraging results suggest that such a unique CuCo2O4@MnO2 CAs architecture could be considered as one of the most promising candidates for energy storage devices with higher energy density delivery.