Positive electrode active material for non-aqueous electrolyte secondary battery having rare earth h

In a non-aqueous electrolyte secondary battery including a positive electrode 1, a negative electrode 2 and a non-aqueous electrolyte, a positive electrode active material wherein a particle of at least one compound selected from Er hydroxide, Er oxyhydroxide, Yb hydroxide, Yb oxyhydroxide, Tb hydroxide, Tb oxyhydroxide, Dy hydroxide, Dy oxyhydroxide, Ho hydroxide, Ho oxyhydroxide, Tm hydroxide, Tm oxyhydroxide, Lu hydroxide, and Lu oxyhydroxide is dispersed and adhered on a surface of a positive electrode active material particle containing Li is used.