In this study, CuCo2S4 directly grown on carbon fiber papers (CFP) were prepared by a low-cost hydrothermal method. We also studied the influence of two different sulfur sources on the morphology and performance of CuCo2S4. Compared to TAA as sulfur source, the performance and morphology of CuCo2S4 by Na2S·9H2O are better. The CuCo2S4–Na2S nanotubes possess irregular diameters from 100 to 200 nm. An electrode made of the synthesized CuCo2S4–Na2S nanotubes/CFP composite exhibits a maximum specific capacitance of 456 F g−1 at 1 A g−1 and 83% of capacitance retention after 5000 cycles at 5 A g−1. The synthesized CuCo2S4–Na2S/CFP is used to construct an all-solid-state asymmetric supercapacitor (ASC) as the positive electrode, while and the negative electrode is made of a Fe2O3/reduced graphene oxide (rGO) composite on Ni foam. This asymmetric device has delivered an energy density of 50 W h kg−1 and a power density of 700 W kg−1 at an operating voltage of 1.5 V. It retains a long cycling life—78.2% capacity retention ratio after 5000 cycles. This work demonstrates the feasibility of the CuCo2S4–Na2S nanotubes in the applications of high-performance supercapacitors.