Disclosed is a positive electrode active material powder composed of primary particles and aggregated particles wherein primary particles aggregate. The volume-average particle diameter of the primary particles and aggregated particles in the powder is not less than 0.1 [mu]m but not more than 3 [mu]m; the percentage of [volume sum of particles having a particle diameter of not less than 5 [mu]m]/[volume sum of all particles] is not more than 10%; and the BET specific surface area of the powder is more than 2 m<2>/g but not more than 7 m<2>/g. When this positive electrode active material powder is used in a nonaqueous electrolyte secondary battery, high discharge capacity is obtained and high output is achieved at high current rate.