The object of the present invention is to improve the roundness of nickel-manganese composite hydroxide particles obtained by a crystallization process, and to improve the filling characteristic of cathode active material produced using the nickel-manganese composite hydroxide particles as a precursor. A reaction aqueous solution is formed by supplying a raw material aqueous solution including at least Ni and Mn, an aqueous solution including an ammonium-ion donor, and an alkali solution into a reaction tank, and mixing, then nickel-manganese composite hydroxide particles are crystallized. When doing this, the oxygen concentration inside the reaction tank is controlled to be 3.0% by volume or greater, the temperature of the reaction aqueous solution is controlled to be 35° C. to 60° C., and the nickel-ion concentration is controlled to be 1,000 mg/L or greater. As a result, nickel-manganese composite hydroxide particles are obtained that include secondary particles formed by an aggregation of plural primary particles and expressed by the general formula: NixMnyMt(OH)2+α (where 0.05≤x≤0.95, 0.05≤y≤0.95, 0≤t≤0.20, x+y+t=1, 0≤α≤0.5, and M is one or more elements selected from among Co, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta and W); and the average value of the roundness of cathode active material having a particle size that is 70% the average particle size or more is 0.82 or greater, and the tap density is 2.20 g/cm3 or greater.