In this study, the projected density of states (PDOS) of the stable normal-spinel structure and stable Mg/Co mixed-cation spinel structure of Mg 1+y Co 2-x Mn x O 4 (x = 0, 0.5; y = 0, 0.5, 1) in the pristine and discharged states are obtained using first-principles calculations. The spin state and the valence state of the transition metals are investigated. The overlaps of the d orbitals of the transition metals and the p orbitals of oxygen are large, and the covalency between the transition metal and oxygen is strong in the pristine MgCo 2 O 4 and MgCo 1.5 Mn 0.5 O 4. The M-O 6 (M = Co, Mn) octahedra become stable as a host structure. From the PDOS spectra, Co atoms are in the trivalent low-spin state in pristine MgCo 2 O 4 and MgCo 1.5 Mn 0.5 O 4 and Mn atoms are nearly tetravalent in pristine MgCo 1.5 Mn 0.5 O 4. In the discharge process, the overlap of the d orbitals of the transition metals and the p orbitals of oxygen becomes narrow and the valence of the transition metals decreases with increasing Mg insertion. The results of the first-principles calculations are consistent with those of X-ray absorption near edge structure spectra.