A method for producing a nickel cobalt complex hydroxide includes first crystallization of supplying a solution containing Ni, Co and Mn, a complex ion forming agent and a basic solution separately and simultaneously to one reaction vessel to obtain nickel cobalt complex hydroxide particles, and a second crystallization of, after the first crystallization, further supplying a solution containing nickel, cobalt, and manganese, a solution of a complex ion forming agent, a basic solution, and a solution containing said element M separately and simultaneously to the reaction vessel to crystallize a complex hydroxide particles containing nickel, cobalt, manganese and said element M on the nickel cobalt complex hydroxide particles crystallizing a complex hydroxide particles comprising Ni, Co, Mn and the element Mon the nickel cobalt complex hydroxide particles.