NOVELTY - A positive electrode active material has a structure comprising lithium complex oxide (1) whose surface is coated with substance (A) consisting of particles. The substance is a compound chosen from zirconium, aluminum, niobium and zinc. In the particle-size distribution curve of the lithium complex oxide, it has particle size distribution, where the average particle diameter (D50) which means the particle size the accumulation frequency of whose is 50%, is 3-15 mu m, the minimum particle size is 0.5 mu m or more, and the maximum particle size is 50 mu m or less.    USE - Positive electrode active material is used for non-aqueous-electrolyte secondary battery used as vehicle-mounted power supply for hybrid vehicle, electric appliance, tool and backup power supply device for backup.    ADVANTAGE - The positive electrode active material has excellent charge-and-discharge capacitance, cycle characteristics and output characteristics.    DETAILED DESCRIPTION - A positive electrode active material has structure comprising lithium complex oxide whose surface is coated with substance (A) consisting of particles. The substance (A) is a compound chosen from titanium, tin, magnesium, zirconium, aluminum, niobium and zinc. In the particle-size distribution curve of the lithium complex oxide, it has particle size distribution, where the average particle diameter (D50) which means the particle size the accumulation frequency of whose is 50%, is 3-15 mu m, the minimum particle size is 0.5 mu m or more, and the maximum particle size is 50 mu m or less. In a relationship of average particle diameter (D50) and the particle size (D10) of 10% of accumulation frequency and 90% of particle size (D90), is 0.60-0.90. The ratio of particle size (D10) and particle size (D90) is 0.30-0.70. The lithium complex oxide is of formula (1): LixNi(1-y-z-a)CoyMnzMaO2.    M=iron, vanadium, chromium, titanium, magnesium, aluminum, calcium, niobium and/or zirconium;    x=1-1.10;    y+z=0.4-0.7;    z=0.2-0.5;and    a=0-0.2.