The present invention relates to lithium manganate particles having a primary particle diameter of 1 to 8 μm and forming substantially single-phase particles, which have a composition represented by the following chemical formula: Li1+xMn2−x−yY1yO4+Y2 in which Y1 is at least one element selected from the group consisting of Ni, Co, Mg, Fe, Al, Cr and Ti; Y2 is P and is present in an amount of 0.01 to 0.6 mol % based on Mn; and x and y satisfy 0.03≦x≦0.15 and 0.05≦y≦0.20, respectively, and which lithium manganate particles have a specific surface area of the lithium manganate particles of 0.3 to 0.9 m2/g (as measured by BET method); and have an average particle diameter (D50) of the lithium manganate particles of 3 to 10 μm. A positive electrode active substance of a lithium ion secondary battery using the lithium manganate particles of the present invention has a high output and is excellent in high-temperature stability.