Positive electrode active material for non-aqueous electrolyte secondary battery and production method for same, precursor for positive electrode active material, and non-aqueous electrolyte secondary battery using positive electrode active material

Provided is a cathode active material for a non-aqueous electrolyte secondary battery capable of obtaining high initial discharge capacity and good output characteristics at low temperature. In order to achieve this, a cathode active material that is a lithium nickel composite oxide composed of secondary particles that are an aggregate of primary particles is expressed by the general expression: Li w (Ni 1-x-y Co x Al y ) 1-z M z O 2 (where 0.98≦w≦1.10, 0.05≦x≦0.3, 0.01≦y≦0.1, 0≦z≦0.05, and M is at least one metal element selected from a group consisting of Mg, Fe, Cu, Zn and Ga), and where the crystallite diameter at (003) plane of that lithium nickel composite oxide that is found by X-ray diffraction and the Scherrer equation is within the range of 1200 {acute over (Å)} to 1600 {acute over (Å)} is used as the cathode material.