Transition-metal sulfide is a good kind of material for supercapacitors because of the large capacity. Nevertheless, the low electroconductivity, slow reaction kinetics, and limited active centers lead to poor electrochemical properties such as long-term cycling stability. In the present work, nano nickel metal-organic framework (Ni-MOF) was constructed by using the nitrogen-rich functional group ligand 2,4,6-tris(3,5-dicarboxylphenylamino)-1,3,5-triazin and compounded with carbon nanotubes (CNTs) to prepare Ni-MOF/CNTs composite, which was used as a precursor to prepare the MOFs-derived NC/Ni-Ni3S4/CNTs composite with the Ni3S4 uniformly distributed in the three-dimensional (3D) conductive network. The rich nitrogen doping and 3D conductive network constructed by CNTs improved the conductivity, prompted the rapid entry of electrolyte, and improved the reaction kinetics of NC/Ni-Ni3S4/CNTs, thus obtained excellent specific capacitance, coulomb efficiency, and cyclic stability. The specific capacitance of NC/Ni-Ni3S4/CNTs is 1489.9 F/g at 1 A/g, which remains 800 F/g at 10 A/g, showing good rate performance.