NOVELTY - Nickel-cobalt composite hydroxide (I) having average particle diameter (D50) of 4-25 mu m and specific surface area of 1 m2/g or more and less than 8 m2/g, and lithium compound are mixed and baked, to obtain active material. Nickel-cobalt composite hydroxide is prepared by mixing aqueous solution containing nickel salt and/or cobalt salt and aqueous solution containing ammonium-ion supply component, supplying caustic-alkali aqueous solution, adjusting pH, reducing transition metal ion concentration, separating the reaction solution into solid and liquid, washing solid and drying.    USE - Manufacture of active material used for positive electrode of nonaqueous electrolyte secondary battery. Uses include but are not limited to mobile telephone, notebook-type personal computer, electric vehicles and hybrid motor vehicles.    ADVANTAGE - The method enables manufacture of positive-electrode active material having excellent thermal stability with high productivity. The outflow of transition metal from the positive-electrode active material can be suppressed. The positive electrode containing the active material provides nonaqueous electrolyte secondary battery having excellent cycle characteristics and output characteristics.    DETAILED DESCRIPTION - Nickel-cobalt composite hydroxide of formula: Ni1-x-y-zCoxMnyMz(OH)2 (I) having average particle diameter (D50) of 4-25 mu m measured by laser scattering particle size distribution method and specific surface area of 1 m2/g or more and less than 8 m2/g measured by nitrogen adsorption BET method, and lithium compound are mixed and baked at 800-1000 degrees C, to obtain positive-electrode active material. Nickel-cobalt composite hydroxide is prepared by mixing aqueous solution containing nickel salt and/or cobalt salt and aqueous solution containing ammonium-ion supply component, supplying caustic-alkali aqueous solution continuously, crystallizing nickel-cobalt composite hydroxide particles by adjusting pH of the reaction solution to 10-12 at 25 degrees C, supplying caustic-alkali aqueous solution, adjusting pH of the reaction solution to 12.5 or more at 25 degrees C, reducing transition metal ion concentration in the reaction solution, separating the reaction solution containing the pH-controlled nickel-cobalt composite hydroxide particles into solid and liquid, washing the nickel-cobalt composite hydroxide particles, and drying.    x=more than 0 and 0.5 or less;    y=0 or more and less than 0.5;    z=0-0.1;and    M=element chosen from Mg, Al, Ca, Ti, V, Cr, Zr, Nb, Mo and W.