The present invention provides a positive electrode active material for a non-aqueous electrolyte-based secondary battery, composed of a lithium/nickel composite oxide with high capacity, low cost and excellent heat stability, an industrially suitable production method therefor, and a high safety non-aqueous electrolyte-based secondary battery. A lithium/nickel composite oxide is produced by the following steps (a) to (c): (a) Nickel hydroxide or nickel oxyhydroxide having a specified component is prepared at a temperature of 600 to 1100° C., under air atmosphere. (b) Fired powders are prepared after mixing said nickel oxide and a lithium compound, and then by firing at a maximal temperature range of 650 to 850° C., under oxygen atmosphere. (c) Obtained fired powders are washed with water within a time satisfying the following equation (2) and then filtered and dried. A≦B/40   (2) wherein, A represents washing time represented by unit of minute; and B represents slurry concentration represented by unit of g/L).