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) LipQxMyOzFa (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≦p≦1.1, 0.980≦x≦1.000, 0≦y≦0.02, 1.9≦z≦2.1, x+y=1, and 0≦a≦0.02, and when Q is Mn, 1≦p≦1.3, x=2−y, 0≦y≦0.05, z=4, and a=0), having an average particle size D50 of from 5 to 30 μm, and having a compression breaking strength of at least 40 MPa; and a second composite oxide powder represented by the formula (2) LipNixCoyMnzNqOrFa (wherein N is aluminum or an alkaline earth metal element or a transition metal element other than Ni, Co and Mn, 0.9≦p≦1.1, 0.2≦x≦0.8, 0≦y≦0.4, 0≦z≦0.5, 0≦q≦0.05, 1.9≦r≦2.1, x+y+z+q=1, and 0≦a≦0.02), having an average particle size D50 of from 2 to 30 μm, 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.