The cubic spinel structures, TiS2 and LiTI2S4, have been fully optimized using the full-potential linearized augmented-plane-wave (LAPW) method. The comparison between band structures of TiS2 and LiTi2S4 and the analogous oxide structures indicates that bonding in sulfides is more covalent. Bonding of both sulfides and oxides becomes more ionic after Li intercalation. The calculated average intercalation voltage of 2.16 eV (LiTi2S4) and 2.93 eV (LiTi2O4) is in good agreement with experimental data. The higher voltage of oxide is due to the larger change of enthalpy of formation between reactants and products.