Abstract: The present invention provides positive electrode active substance particles comprising a lithium nickelate composite oxide which have a high energy density and are excellent in repeated charge/discharge cycle characteristics when charging at a high voltage, as well as a non-aqueous electrolyte secondary battery. The present invention relates to positive electrode active substance particles each comprising a core particle X comprising a lithium nickelate composite oxide having a layer structure which is represented by the formula: Li1+aNi1-b-cCobMcO2 wherein M is at least one element selected from the group consisting of Mn, Al, B, Mg, Ti, Sn, Zn and Zr, a is a number of ?0.1 to 0.2 (?0.1·a·0.2), b is a number of 0.05 to 0.5 (0.05·b·0.5) and c is a number of 0.01 to 0.4 (0.01·c·0.4); and a coating compound Y comprising at least one element selected from the group consisting of Al, Mg, Zr, Ti and Si and having an average film thickness of 0.