An essential way to enhance the energy density of a supercapacitor(SC) is to use high capacitance electrode materials via developing binder-free electrode with porous and hierarchical nanostructures. Herein, we demonstrated the use of copper antimony sulfide (Cu3SbS4) nanowires directly grown on Ni foam (using a microwave-irradiation process) as a binder-free positive electrode for SCs. The growth mechanism, effect of microwave irradiation time on the morphology and electrochemical properties of Cu3SbS4 on Ni foam were discussed in detail. The cyclic voltammetric studies (using three-electrode test) of Cu3SbS4/Ni-5 electrode showed the presence of Type-C battery-like charge-storage properties. The Cu3SbS4/Ni-5 electrode delivered a high specific capacity (835.24 mA h g−1) as obtained from the charge-discharge analysis (at a current density of 2.5 mA cm−2). Further, the device specific properties of the Cu3SbS4/Ni-5 positive electrode was examined via fabricating asymmetric supercapacitors (ASCs) using two different negative electrodes viz. (i) planar-graphene, and (ii) binder-free copper molybdenum sulfide anchored on Ni foam (Cu2MoS4/Ni) electrodes, respectively. The electrochemical analyses of the fabricated ASCs revealed that the Cu3SbS4/Ni-5║Cu2MoS4/Ni ASC possess almost 3.0-fold higher energy density compared to the Cu3SbS4/Ni-5║graphene ASC. The Cu3SbS4/Ni-5║Cu2MoS4/Ni ASC delivered a high specific device capacitance of 213.6 F g−1 with a remarkable energy density (58.15 Wh kg−1), maximum power density (6363.63 W kg−1), and better cycle-life. The use of two different binder-free electrodes in the Cu3SbS4/Ni-5║Cu2MoS4/Ni ASC results in their superior performance metrics over the reported ASCs, thus, highlighting their potential applications towards next-generation supercapacitors.