NOVELTY - A positive electrode active material comprises secondary particles composed of fine secondary particles having average particle diameter of 2-4 mu m, and coarse secondary particles having average particle diameter of 6-15 mu m. The secondary particles have average particle diameter of 5-15 mu m. The fine secondary particles comprise a lithium-nickel composite oxide to which at least two metal elements including aluminum are added. The molar ratio of aluminum concentration in fine secondary particles and coarse secondary particles is 1.12-2.6.    USE - Positive electrode active material for positive electrode material of non-aqueous electrolyte secondary battery (claimed) used as power supply for hybrid vehicle, motor vehicle and electric vehicle. Uses include but are not limited to mobile telephone, video camera, handheld terminal, gasoline engine, diesel engine, etc.    ADVANTAGE - The non-aqueous electrolyte secondary battery formed using the positive electrode active material has high safety, high durability, and high charge/discharge capacity.    DETAILED DESCRIPTION - A positive electrode active material comprises secondary particles composed of fine secondary particles having average particle diameter of 2-4 mu m, and coarse secondary particles having average particle diameter of 6-15 mu m. The secondary particles have average particle diameter of 5-15 mu m. The fine secondary particles comprise a lithium-nickel composite oxide to which at least two metal elements including aluminum are added. The molar ratio of aluminum content in the fine secondary particles is more than the aluminum content in the coarse secondary particles. The molar ratio of aluminum concentration in fine secondary particles and coarse secondary particles is 1.12-2.6. The particle size distribution of fine secondary particles with size of 0.5-6 mu m, and coarse secondary particles with size of 3-25 mu m, is observed by laser diffraction scattering method. An INDEPENDENT CLAIM is included for manufacture of positive electrode active material. An aluminum compound is added and mixed with a nickel composite hydroxide. Oxidizing roasting of obtained aluminum-containing nickel composite hydroxide is carried out. Lithium compound is further added and mixed with obtained product, and obtained mixture is baked. Thus, positive electrode active material is obtained.