Aluminum-coated nickel cobalt containing composite hydroxide and method for manufacturing same, cathode active material for non-aqueous electrolyte secondary battery and method for manufacturing same, and non-aqueous electrolyte secondary battery

Provided is a cathode active material for a non-aqueous electrolyte secondary battery that improves the cycling characteristic and high-temperature storability without impairing the charge/discharge capacity and the output characteristics. A nickel cobalt containing composite hydroxide is obtained by using a batch type crystallization method in which a raw material aqueous solution that includes Ni, Co and Mg is supplied in an inert atmosphere to a reaction aqueous solution that is controlled so that the temperature is within the range 45° C. to 55° C., the pH value is within the range 10.8 to 11.8 at a reference liquid temperature of 25° C., and the ammonium-ion concentration is within the range 8 g/L to 12 g/L. An Al-coated composite hydroxide that is expressed by the general formula: Ni1-x-y-zCoxAlyMgz(OH)2 (where, 0.05≤x≤0.20, 0.01≤y≤0.06, and 0.01≤z≤0.03) is obtained by mixing a slurry that includes the nickel cobalt containing composite hydroxide with a coating aqueous solution that includes Al to form a mixed aqueous solution, and coating the secondary particles with a coating film that includes Al or an Al compound. A cathode active material that is configured so that component elements that include Al are uniformly dispersed in the secondary particles is synthesized using the Al-coated composite hydroxide as a precursor.