A non-aqueous electrolyte secondary battery has a positive electrode containing a positive electrode active material, a negative electrode containing a negative electrode active material, and a non-aqueous electrolyte. The positive electrode active material includes a lithium-nickel-manganese composite oxide having a hexagonal layered rock-salt structure that belongs to the space group R-3m, and contains lithium in 3b sites that contain transition metals. The lithium-nickel-manganese composite oxide is represented by the molecular formula Li[LixNiyMnzMb]O2-a where: 0 (1−2y)/3, 1/4≦y/z≦1.0, 0