Abstract: A mixture of a cobalt compound and a lithium compound is calcined at a temperature of 250.degree. C. to 1,000.degree. C., where said cobalt compound has a cobalt content of 68.5.+-.6% by weight, its composition is substantially represented by a formula H.sub.x CoO.sub.y provided that 0.ltoreq.x.ltoreq.1.4 and 1.3.ltoreq.y.ltoreq.2.2, the half value width of a diffraction peak showing a maximum intensity in the neighborhood of 2.theta.=36-40 degrees in X-ray diffraction using CuK.alpha. as a radiation source is greater than 0.31 degrees, and the relation between the cobalt content and the half value width is represented by the following formula:Half value width (degrees).gtoreq.7.5-0.1.times.(Cobalt content) (% by weight). This provides an inexpensive and simple process for producing a lithium-cobalt composite oxide having uniform crystals, and a high-performance electrode active material for use in lithium secondary cells in high capacity and excellent in the charging-discharging cycle characteristics.