The present invention provides a lithium secondary battery having a great output power in a low SOC range and a positive electrode active material for use in the battery The battery comprises a positive electrode, a negative electrode and a non-aqueous electrolyte. The positive electrode comprises a positive electrode active material in a form of secondary particles as aggregates of primary particles of a lithium transition metal oxide. The positive electrode active material comprises at least one species of Ni, Co and Mn, and further comprises W and Mg. The W is present, concentrated on surfaces of the primary particles while the Mg is present throughout the primary particles. The Mg content in the positive electrode active material is higher than 50 ppm relative, to the total amount of the active material based on the mass.