To provide a process for producing a lithium-cobalt composite oxide for a positive electrode of a lithium secondary battery excellent in volume capacity density, safety, charge and discharge cyclic durability, press density and productivity, by using in expensive cobalt hydroxide and lithium carbonate. A mixture having a cobalt hydroxide powder and a lithium carbonate powder mixed so that the atomic ratio of lithium/cobalt would be from 0.98 to 1.01, is fired in an oxygen-containing atmosphere at from 250 to 700.degree. C., and the fired product is further fired in an oxygen-containing atmosphere at from 850 to 1,050.degree. C., or such a mixture is heated at a temperature-raising rate of at most 4.degree. C./min in a range from 250 to 600.degree. C. and fired in an oxygen-containing atmosphere at from 850 to 1,050.degree. C.