A lithium-manganese composite oxide for a lithium ion battery having a good cycle property at high-temperature and battery property of high capacity is provided. A spinel type lithium-manganese composite oxide for a lithium ion battery represented by a general formula: Li1+xMn2-yMyO4 (wherein M is one or more elements selected from Al, Mg, Si, Ca, Ti, Cu, Ba, W and Pb, and, −0.1≦x≦0.2, and 0.06≦y≦0.3), and when D10, D50 and D90 are defined as a particle size at which point the cumulative frequency of volume reaches 10%, 50% and 90% respectively, d10 is not less than 2 μm and not more than 5 μM, d50 is not less than 6 μm and not more than 9 μm, and d90 is not less than 12 μm and not more than 15 μM, and BET specific surface area thereof is greater than 1.0 m2/g and not more than 2.0 m2/g, and the tap density thereof is not less than 0.5 g/cm3 and less than 1.0 g/cm3.