Rational construction of three dimensional (3D) composite structure is an important method to flexible supercapacitor electrodes and has been extensively developed. In this work, a 3D self-supported CuCo2S4@NiCo2S4 core-shell nanostructure grown on Nickel (Ni) foam, constructed by a hydrothermal method, was used as a novel supercapacitor electrode material. The unique structure possesses a large, specific surface area, rapid diffusion of electrolyte ions by numerous channels and avoids the use of additives and adhesives. The high electrical conductivity of the CuCo2S4 nanoneedle arrays can speed up electronic transmission. At a current density of 1 A g-1, the electrode material exhibits a high specific capacity of 539.2 C g-1 and cycling stability with 100% capacity retention after 5000 cycles in 3 M KOH. Furthermore, when the obtained CuCo2S4@NiCo2S4 was used as the positive electrode and an activated carbon was used as the negative electrode, a solid-state asymmetric supercapacitor was assembled. More importantly, the obtained solid-state asymmetric supercapacitor demonstrated excellent electrochemical performance. When the power density was 400 W kg-1, it delivered a high density of 23.4 W h kg-1 with a high voltage window of 1.6 V, thus demonstrating that the material has the potential for use as an efficient electrode for electrochemical capacitors. Due to its comprehensive electrochemical performance, the CuCo2S4@NiCo2S4 solid-state asymmetric supercapacitor effectively operated a red LED.