A method for manufacturing LiMn2O4 powders for use in a lithium secondary battery positive electrode, is provided, in which oxide or carbonate is used as a positive electrode material, a solution is dried at a temperature higher than 150° C., and the resulting matter is put into a reaction furnace in order to be calcinated for a short time, after treating by spontaneous combustion. A certain degree of crystallization of the positive electrode powders can be obtained in the spontaneous combustion process. Thus, a battery having a large charging and discharging capacity and a long life cycle can be manufactured even under a high current condition.