The present invention relates to a method for preparing a lithium manganese complex oxide Li_1+xMn_2-;xO₄ (0x0.12) used as a cathode active material of a lithium or lithium ion secondary battery. The present invention provides a method for preparing a manganese compound comprising the step of simultaneously applying a mechanical force and heat energy to a manganese compound to remove defects present in particles of the manganese compound and to control the aggregation of particles and the shape of the aggregated particles, a method for preparing a lithium manganese complex oxide with a spinel structure using the manganese compound prepared by the above method as a raw material, and a lithium or lithium ion secondary battery using the lithium manganese complex oxide with a spinel structure prepared by the above method as a cathode active material. A lithium or lithium ion secondary battery using the lithium manganese complex oxide with a spinel structure prepared from the manganese compound without defects inside particles as a cathode active material has excellent charge/discharge characteristics and cyclic performance.