A positive-electrode active material contains a compound that has a crystal structure belonging to the space group FM3-M and that is represented by the composition formula (1): LixMeyOαFβ  (1) wherein Me denotes one or two or more elements selected from the group consisting of B, Ce, Si, Zr, Nb, Pr, Ti, W, Ge, Mo, Sn, and solid solutions thereof, and the following conditions are satisfied. 1.8≦x≦2.2 0.8≦y≦1.3 1.2≦α≦2.5 0.5≦β≦1.8