A positive electrode active material for a non-aqueous-electrolyte secondary battery contains a nickel-containing lithium transition metal oxide and is a primary particle alone of a lithium transition metal oxide that contains nickel in an amount of 80 mol % or more relative to the whole molar quantity of a metal element other than lithium or a secondary particle formed by aggregation of two to five particles. A rare earth compound and a magnesium compound adhere to the surface of the primary particle alone or the secondary particle.