A positive electrode active material, which gives a non-aqueous electrolyte secondary battery capable of high input/output where resistance due to a battery reaction in a low temperature environment is suppressed, is produced by a method comprising: (a)providing a nickel hydroxide which is represented by the general formula Ni.sub.1-(x+y)Co.sub.xM.sub.y(OH).sub.2, (b)heating the nickel hydroxide at a temperature not lower than 600.degree. C. and not higher than 1000.degree. C. to produce a nickel oxide which is represented by the general formula Ni.sub.1-(x+y)Co.sub.xM.sub.yO; and (c)mixing the nickel oxide and a lithium compound to obtain a mixture and heating the mixture at a temperature not lower than 700.degree. C. and not higher than 850.degree. C. to produce a lithium-containing composite oxide which is represented by the general formula LiNi.sub.1-(x+y)Co.sub.xM.sub.yO.sub.2, where 0.1.ltoreq.x.ltoreq.0.35 and 0.03.ltoreq.y.ltoreq.0.2 are satisfied and M is at least one selected from the group consisting of Al, Ti and Sn.