A method of producing a positive-electrode active material for a non-aqueous electrolyte secondary battery is provided. The method includes obtaining a precipitate containing nickel and manganese from a solution containing nickel and manganese, heat-treating the resulting precipitate at a temperature of from 850° C. to less than 1100° C. to obtain a first heat-treated product, mixing the first heat-treated product and a lithium compound, and heat-treating the resulting lithium-containing mixture at a temperature of from 550° C. to 1000° C. to obtain a second heat-treated product. The second heat-treated product contains a group of lithium transition metal composite oxide particles having an average particle diameter DSEM of from 0.5 μm to less than 3 μm and D50/DSEM of 1 to 2.5. The lithium transition metal composite oxide particles have a spinel structure based on nickel and manganese.