Composite electrodes that possess both rational structures and appropriate integration are needed to deliver high electrochemical performance in energy storage devices. In this paper, a flexible and binder-free electrode material based on a heterogeneous core-shell structure of CuCo2O4@Ni(OH)(2) nanosheets grown on carbon cloth was fabricated by a simple method. The unique three-dimensional hierarchical structure gives the electrode a large specific surface area, which enables rapid response and increases of specific capacitance. The CuCo2O4@Ni(OH)(2)/carbon fiber cloth (CFC) composite electrode exhibited a specific capacitance of 2160 F g(-1) at 1 A g(-1) and a good rate capability energy of 82.7% at 20 A g(-1). A flexible all-solid-state asymmetric supercapacitor (FAASC) was assembled with the CuCo2O4@Ni(OH)(2)/CFC electrode as the positive electrode, and activated carbon (AC)/CFC as the negative electrode. This device showed both a high energy density and power density (58.9 W h kg(-1) at a power density of 400 W kg(-1)), and good long-term cycling stability. Furthermore, the assembled CuCo2O4@Ni (OH)(2)/CFC//AC/CFC devices were capable of driving a blue light-emitting diode after a short charge. The remarkable performance of this CuCo2O4@Ni(OH)(2)/CFC electrode indicates that this heterogeneous structure has great potential for applications in flexible high-performance energy storage devices. (C) 2019 Elsevier Inc. All rights reserved.