Abstract: A lithium-manganese composite oxide represented by formula (1): Li1+x[(FeyNi1?y)zMn1?z]1?xO2 (1) wherein x, y, and z satisfy the following: 0<x??, 0?y<1.0, and 0<z?0.6, and wherein the content ratio of Li to the total content of Fe, Ni, and Mn (Li/(Fe+Ni+Mn)) is 1.55 or less on a molar ratio basis, the lithium-manganese composite oxide containing a crystalline phase having a layered rock-salt structure. This composite oxide is a novel material made from less resource-constrained and cheaper elements, and exhibits a high specific capacity, excellent charge-and-discharge cycle characteristics, and a high discharge capacity at a high current density (excellent rate characteristics), when used in the positive electrode material for lithium-ion secondary batteries.