To provide a process for producing a lithium-cobalt composite oxide for a positive electrode of a lithium secondary battery, which has a large volume capacity density, high safety, high charge and discharge cycle durability, high press density and high productivity.A process for producing a lithium-cobalt composite oxide represented by the formula Li.sub.pCo.sub.xM.sub.yO.sub.zF.sub.a (wherein M is a transition metal element other than Co, or an alkaline earth metal element, 0.9.ltoreq.p.ltoreq.1.1, 0.980.ltoreq.x.ltoreq.1.000, 0.ltoreq.y.ltoreq.0.02, 1.9.ltoreq.z.ltoreq.2.1, x+y=1, and 0.ltoreq.a.ltoreq.0.02), characterized in that as a cobalt source, a mixture is used which comprises cobalt hydroxide in the form of substantially spherical secondary particles with an average particle size of from 8 to 20 .mu.m formed by agglomeration of primary particles and tricobalt tetroxide in the form of secondary particles with an average particle size of from 2 to 10 .mu.m formed by agglomeration of primary particles, in a cobalt atomic ratio of from 5:1 to 1:5, and firing is carried out at from 700 to 1,050.degree. C.