The volume density or weight density of lithium ions that can be received and released in and from a positive electrode active material is increased to achieve high capacity and high energy density of a secondary battery. In a lithium manganese composite oxide, each particle includes a first region including a crystal with a layered rock-salt crystal structure and a second region including a crystal with a spinel crystal structure. The second region is in contact with the outside of the first region. The lithium manganese composite oxide has high structural stability and high capacity.