Provided are nickel manganese composite hydroxide particles that are a precursor for forming cathode active material comprising lithium nickel manganese composite oxide having hollow structure of particles having a small and uniform particle size for obtaining a non-aqueous electrolyte secondary battery having high capacity, high output and good cyclability.When obtaining the nickel manganese composite hydroxide particles from a crystallization reaction, an aqueous solution for nucleation, which includes at least a metallic compound that contains nickel and a metallic compound that contains manganese, and does not include a complex ion formation agent that forms complex ions with nickel, manganese and cobalt, is controlled so that the temperature of the solution is 60° C. or greater, and so that the pH value that is measured at a standard solution temperature of 25° C. is 11.5 to 13.5, and after nucleation is performed, an aqueous solution for particle growth, which includes the nuclei that were formed in the nucleation step and does not substantially include a complex ion formation agent that forms complex ions with nickel, manganese and cobalt, is controlled so that the temperature of the solution is 60° C. or greater, and so that the pH value that is measured at a standard solution temperature of 25° C. is 9.5 to 11.5, and is less than the pH value in the nucleation step.