To provide a positive electrode active material capable of simultaneously improving the capacitance characteristic, output characteristic, and cycle characteristic of a non-aqueous electrolyte secondary battery when being used as a positive electrode material of the secondary battery. [Solution] After an aqueous solution for nucleation which contains a metallic compound containing at least transition metal and an ammonium ion supplier is controlled to have a pH value of 12.0-14.0 to form nuclei (a nucleation step), the pH value of an aqueous solution for particle growth which contains the nuclei is controlled to become lower than the pH value in the nucleation step and become 10.5-12.0 to thereby grow the nuclei (a particle growth step). In this case, atmosphere control in which the initial stages of the nucleation step and the particle growth step are performed in a non-oxidizing atmosphere, and in the particle growth step, after switching from the non-oxidizing atmosphere to an oxidizing atmosphere, switching again to the non-oxidizing atmosphere is done is performed at least once. Composite hydroxide particles obtained by the abovementioned crystallization reaction are used as a precursor to obtain a positive electrode active material.