A life of a secondary battery is extended, increase in a resistance when storing a secondary battery at an elevated temperature is prevented, and increase in a resistance during a charge-discharge cycle is prevented. A positive electrode active material comprising a lithium manganate and a lithium nickelate are used. The lithium manganate is a compound represented by the following formula (1) or the compound in which some of Mn or O sites are replaced with another element: Li.sub.1+xMn.sub.2-xO.sub.4 (1) (in the above-shown formula (1), 0.15.ltoreq.x.ltoreq.0.24).