Display omitted •The influence of the different anions on the electrochemical performance of Co3X4 is studied and analyzed with DFT.•Co3O4 and Co3Se4 are synthesized with a simple novel two-step hydrothermal method, which will be applied for the synthesis of electrical materials with specific structure.•The redox reactions of Co3O4 during the charge–discharge process are obtained.•Co3Se4 shows better performance than Co3O4 due to the morphology and conductivity. In order to investigate the influence of the anions on the electrochemical performance of cobalt-based compounds, Co3O4 and Co3Se4 are studied and theoretically analyzed with the density functional theory (DFT). Avoiding of the traditional synthesis of the high-temperature annealing for the transition metal oxides, the cubic spinel phase Co3O4 on a nickel foam (NF) substrate with a simple two-step hydrothermal method and Co3Se4 with the core-branched structure by anions exchange method are prepared. The electrochemical measurements show that the capacitance and conductivity of Co3Se4 are significantly better than those of Co3O4, and Co3Se4 still maintain high capacity at high current density. Furthermore, the kinetics of electrode material Co3O4 and Co3Se4 are analyzed and compared. According to the calculation of the density of states, the results show the band gap of Co3O4 is 2.18 eV and the Fermi energy line of Co3Se4 enters into the conduction band, which means the conductivity of Co3Se4 is better than that of Co3O4. Additionally, three redox reactions during the charge and discharge process of Co3O4 are determined and the band gaps changes are also calculated.