Flexible asymmetric supercapacitor (FASC) systems are expected to exhibit not only excellent energy storage properties and safety but also satisfactory flexibility and robust integration. However, tremendous issues such as low capacitance, narrow voltage window, and poor mechanical properties still exist. In this paper, a novel kind of 3D lamellar Mn(OH) 2 nanosheets on Cu-plated carbon cloth with a core-shell integrated framework (CPCC@CuO@Mn(OH) 2 ) is fabricated to obtain the flexible material in the FASC. In this unique CPCC@CuO@Mn(OH) 2 electrode material, the high theoretical specific capacity of CuO and Mn(OH) 2 brings superior energy storage properties. Meanwhile, as the shell part, the deposited Mn(OH) 2 layer and coated CuO layer work as both capacity contributors and substrate protectors, simultaneously maintaining the high capacitance and satisfactory flexibility of the electrodes. Therefore, the capacitance successfully achieves around 8140 mF cm −2 under 0.5 mA cm −2 . Significantly, the assembled FASC (named as CPCC@CuO@Mn(OH) 2 //CC@AC) achieves a working voltage of up to 2.4 V. In the case of a high-power density close to 34.31 mW cm −3 , its energy density reaches around 6.29 mW h cm −3 . Moreover, the capacity holds 88.9% even after 10,000 cycles, showing its great application potential in the field of wearable electronics.