Provided is spinel-type lithium transition metal oxide (LMO) used as a positive electrode active material for lithium battery, said LMO being capable of simultaneously achieving all output characteristics (rate characteristics), high temperature cycle life characteristics, and rapid charging characteristics. The disclosed is spinel-type lithium transition metal oxide including, besides Li and Mn, one or more elements selected from a group consisting of Mg, Ti, Ni, Co, and Fe, and having crystallite size of between 200 nm and 1000 nm and strain of 0.0900 or less. Because the crystallite size is markedly large, oxygen deficiency is markedly little, and the structure is strong, when the LMO is used as a positive electrode active material for lithium secondary batteries, all output characteristics (rate characteristics), high temperature cycle life characteristics, and rapid charging characteristics can be achieved simultaneously.