To push the energy density limit of supercapacitors, proper pseudocapacitive materials with favorable nanostructures are urgently pursued. Ternary transition metal sulfides are promising electrode materials due to the better conductivity and higher electrochemical activity in comparison to the single element sulfides and transition metal oxides. In this work, we have successfully synthesized porous CuCo2S4 nanorod array (NRAs) on carbon textile through a stepwise hydrothermal method, including the growth of the Cu-Co precursor nanowire arrays and subsequent conversion into CuCo2S4 NRAs via anion exchange reaction. The CuCo2S4 NRAs electrode exhibits a greatly enhanced specific capacitance and an outstanding cycling stability. Moreover, an asymmetric supercapacitor using the CuCo2S4 NRAs as positive electrode and activated carbon as negative electrode delivers a high energy density of 56.96 W h kg-1. Such superior performance demonstrate that the CuCo2S4 NRAs are promising materials for future energy storage applications.