Lithium composite metal oxides prepared by mixing at least one type of hydroxides, oxides, and carbonates of a metal selected from the group of transition metal, IIA metal, and IIIA metal, and a lithium compound of which the D50 value is in the range 5 to 50 µm, the D90 value is 90 µm or smaller, and in which particles 100 µm or greater do not exist, and calcinating in the temperature range 700 to 1000°C for 2 to 30 hours, and grinding, are used as the active material of a positive electrode which is laminated with a negative electrode with a separator interposed and spirally wound thereby forming an electrode group. By using the positive active materials prepared in this manner, discharge capacity and cycle characteristic of a non-aqueous electrolyte secondary cell can be improved.