It is to provide a cathode active material powder for a positive electrode for a lithium secondary battery, which has a large volume capacity density, high safety and excellent durability for charge and discharge cycles. A cathode active material powder for a lithium secondary battery characterized by comprising a first composite oxide powder represented by the formula (1) Li.sub.pQ.sub.xM.sub.yO.sub.zF.sub.a (wherein Q is Co or Mn, M is aluminum or an alkaline earth metal element or a transition metal element other than Q, provided that when Q is Co, 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, and when Q is Mn, 1.ltoreq.p.ltoreq.1.3, x=2-y, 0.ltoreq.y.ltoreq.0.05, z=4, and a=0), having an average particle size D50 of from 5 to 30 .mu.m, and having a compression breaking strength of at least 40 MPa; and a second composite oxide powder represented by the formula (2) Li.sub.pNi.sub.xCo.sub.yMn.sub.zN.sub.qO.sub.rF.sub.a (wherein N is aluminum or an alkaline earth metal element or a transition metal element other than Ni, Co and Mn, 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, 0.ltoreq.q.ltoreq.0.05, 1.9.ltoreq.r.ltoreq.2.1, x+y+z+q=1, and 0.ltoreq.a.ltoreq.0.02), having an average particle size D50 of from 2 to 30 .mu.m, and having a compression breaking strength less than 40 MPa; in a ratio (weight ratio) of the first composite oxide powder/the second composite oxide powder being from 95/5 to 30/70.