A positive electrode active material is produced by firing, as a cobalt source, a mixture of a) substantially spherical large particle size cobalt hydroxide or tricobalt tetraoxide having a sharp particle size distribution, and b) small particle size cobalt hydroxide or tricobalt tetraoxide, in a proportion of from 9:1 to 1:2 as the cobalt atomic ratio, at a temperature of from 700° C. to 1050° C. in an oxygen-comprising atmosphere.