To provide a lithium-nickel-cobalt-manganese composite oxide powder for a positive electrode of a lithium secondary battery, which has a large volume capacity density and high safety and is excellent in the charge and discharge cyclic durability. A positive electrode active material powder for a lithium secondary battery characterized by comprising a first granular powder having a compression breaking strength of at least 50 MPa and a second granular powder having a compression breaking strength of less than 40 MPa, formed by agglomeration of many fine particles of a lithium composite oxide represented by the formula Li.sub.pNi.sub.xCo.sub.yMn.sub.zM.sub.qO.sub.2-aF.sub.a (wherein M is a transition metal element other than Ni, Co and Mn, Al or an alkaline earth metal element, 0.9.ltoreq.p.ltoreq.1.1, 0.2.ltoreq.x.ltoreq.0.8, 0.ltoreq.y.ltoreq.0.4, 0.ltoreq.z.ltoreq.0.5, y+z>0, 0.ltoreq.q.ltoreq.0.05, 1.9.ltoreq.2-a.ltoreq.2.1, x+y+z+q=1 and 0.ltoreq.a.ltoreq.0.02) to have an average particle size D50 of from 3 to 15 .mu.m, in a weight ratio of the first granular powder/the second granular powder being from 50/50 to 90/10.