A positive electrode active material for a non-aqueous electrolyte battery comprising a lithium-containing transition metal oxide, produced with the use of a dry precursor obtained by: introducing an alkaline solution together with an aqueous solution containing two or more of transition metal salts or two kinds or more of aqueous solutions of different transition metal salts into a reaction vessel to obtain a hydroxide or an oxide as a precursor through coprecipitation with a reductant being coexistent or an inert gas being supplied; and drying the precursor at 300 to 500.degree. C. to obtain a dry precursor.