The amount of lithium ions that can be received and released in and from a positive electrode active material is increased, and high capacity and high energy density of a secondary battery are achieved. Provided is a lithium-manganese composite oxide represented by LixMnyMzOw, where M is a metal element other than Li and Mn, or Si or P, and y, z, and w satisfy 0≦x/(y+z) 0, z>0, 0.26≦(y+z)/w