A positive-electrode active material contains a compound that has a crystal structure belonging to a space group FM3-M and that is represented by the composition formula (1) and a lithium ion conductor, LixMeyOαFβ  (1) wherein Me denotes one or two or more elements selected from the group consisting of Mn, Co, Ni, Fe, Al, B, Ce, Si, Zr, Nb, Pr, Ti, W, Ge, Mo, Sn, Bi, Cu, Mg, Ca, Ba, Sr, Y, Zn, Ga, Er, La, Sm, Yb, V, and Cr, and the following conditions are satisfied. 1.7≤x≤2.2 0.8≤y≤1.3 1≤α≤2.5 0.5≤β≤2