A non-aqueous electrolyte secondary battery having a low manufacturing cost and a high energy density and being excellent in the high rate charge/discharge characteristic and in the characteristics in operation at high temperature provided by an improvement on its positive electrode active material is disclosed. The positive electrode active material comprises a specific compound wherein a part of nickel or lithium in LiNiO.sub.2 is substituted with another element in a specified range. The element for the substitution comprises Mg, Ca, Sr, Ba, Al Cr, B and Co which may be employed solely or in combination.