To improve cycling characteristics of a non-aqueous electrolyte secondary battery by obtaining a nickel-cobalt composite hydroxide having a sharp particle size distribution as a precursor, a slurry including a nickel-cobalt composite hydroxide obtained by continuously supplying an aqueous solution that includes at least nickel and cobalt, an ammonium ion donor aqueous solution and a caustic alkali aqueous solution to a reaction vessel and reacting, is continuously extracted and separated into a large particle size portion and s small particle size portion by classification, and the small particle size portion is continuously returned to the reaction vessel. As a result, a nickel-cobalt composite hydroxide is obtained that is expressed by the general formula: Ni1−x−yCoxMy(OH)2 (where, 0.05≤x≤0.50, 0≤y≤0.10, 0.05≤x+y≤0.50, and M is at least one kind of metal element selected from among Al, Mg, Mn, Ti, Fe, Cu, Zn and Ga, and that satisfies the relationships (D50−D10)/D50≤0.30, and (D90−D50)/D50≤0.30 among D10, D50 and D90 of this composite hydroxide.