The 70Li2S·30P2S5 glass–ceramic showed high ion conductivity of 1.5 × 10−3 S cm−1 at room temperature. The 75Li2S·25P2S5 glass showed ion conductivity of 5.0 × 10−4 S cm−1 at room temperature and high chemical stability. All-solid-state C/LiCoO2 cells using those materials as solid electrolytes were assembled. Their cell performance were compared. The cell using the 70Li2S·30P2S5 glass–ceramic showed superior rate performance to the cell using the 75Li2S·25P2S5 glass. On the other hand, the cell using the 75Li2S·25P2S5 glass showed superior cycle performance to the cell using the 70Li2S·30P2S5 glass–ceramic. It was suggested that solid electrolytes in all-solid-state batteries preferably had both high ion conductivity and high chemical stability.