The present invention industrially provides: a non-aqueous electrolyte secondary battery having a high energy density and high cycling characteristics; a cathode active material for a non-aqueous electrolyte secondary battery having a high packing efficiency; and a nickel manganese containing composite hydroxide having a small particle size, a narrow particle size distribution, and a high sphericity. When producing the nickel manganese containing composite hydroxide by a crystallization reaction using material solution where metal compounds including nickel and manganese dissolve, a nucleation process is performed in a non-oxidizing atmosphere by stirring an aqueous solution for nucleation, that includes the quantity of the material solution corresponding to 0.6% to 5.0% of the whole amount of substance of metal element included in a metal compound used for the overall crystallization reaction.