Manganese composite hydroxide and method for producing same, positive electrode active material and method for producing same, and nonaqueous electrolyte secondary battery

A precursor of a positive electrode active material for a nonaqueous electrolyte secondary battery which can improve the battery characteristic of the nonaqueous electrolyte secondary battery is obtained. A manganese composite hydroxide is obtained by generating a plate crystal nucleus by setting the pH value of a nucleation aqueous solution containing cobalt and/or manganese to 7.5-11.1 based on a solution temperature of 25°C, and then setting the pH value of a particle growth slurry containing the plate crystal nucleus to 10.5-12.5 based on a solution temperature of 25°C and supplying a mixed aqueous solution that includes a metallic compound containing at least manganese to thereby grow the plate crystal nucleus.