NOVELTY - A metal hydroxide containing secondary particles is dispersed in pure water, to form metal-hydroxide slurry. Carbon powder is subjected to ultrasonic dispersion in hot water, to form carbon powder slurry. The metal hydroxide slurry and carbon powder slurry are mixed and filtered. The mixture is heat-processed, to form mixed powder of metal oxide and carbon powder. The mixed powder is mixed with lithium compound and the mixture is baked under oxygen environment, to form lithium-metal complex oxide. Thus, positive-electrode active material is manufactured.    USE - Manufacture of active material used for positive electrode for nonaqueous electrolyte secondary battery (both claimed) used for hybrid vehicles, motor vehicles, electric vehicles, mobile telephone and notebook computer.    ADVANTAGE - The active material is manufactured efficiently, and provides battery with high capacity and excellent battery characteristics.    DETAILED DESCRIPTION - A metal hydroxide containing secondary particles is dispersed in pure water, to form metal-hydroxide slurry. Carbon powder (0.5-1 %mass) is subjected to ultrasonic dispersion processing in hot water at 70 degrees C or more, to form carbon powder slurry. The metal hydroxide slurry and carbon powder slurry are mixed and filtered, to form mixture of metal hydroxide and carbon powder. The obtained mixture is heat-processed in inert gas atmosphere, to form mixed powder of metal oxide and carbon powder. The obtained mixed powder is mixed with lithium compound and the mixture is baked under oxygen environment, to form lithium-metal complex oxide. Thus, positive-electrode active material is manufactured. The secondary particles are obtained by aggregating fine primary particles formed by mixing aqueous solution containing metal ion and alkaline aqueous solution, and neutralizing. The metal hydroxide has average particle diameter of 1-5 mu m. INDEPENDENT CLAIMS are included for the following:    (1) positive-electrode active material, which has average particle diameter of 1-5 mu m; and    (2) non-aqueous electrolyte secondary battery.