NOVELTY - A lithium-nickel complex oxide particles powder comprises a composition containing lithium, nickel, manganese, aluminum, zirconium and magnesium. The metal occupancy rate (%) of the lithium site of lithium-nickel complex oxide particles powder is obtained using Rietveld analysis of X-ray diffraction. The microcrystal size of lithium-nickel complex oxide particles powder is 700-1400 nm, which is obtained using Rietveld analysis.    USE - Lithium-nickel complex oxide particles powder is used for positive electrode material of nonaqueous electrolyte secondary battery (claimed). Uses include but are not limited to hybrid vehicles, electric vehicles, portable electronic devices e.g. audio-video equipment and personal computers.    ADVANTAGE - The lithium-nickel complex oxide particles powder has favorable thermal stability, large crystal size and low specific surface area, ensures diffusion path of lithium, stabilizes crystal structure by controlling the metal site occupancy rate mixed in a lithium site to 2-7%, and provides positive electrode active material with high capacitance. The nonaqueous electrolyte secondary battery consisting of the positive electrode active material has high initial discharge capacity and charging/discharging efficiency.    DETAILED DESCRIPTION - A lithium-nickel complex oxide particles powder comprises a composition of formula: Lix(Ni)(1-y-a-b)CoyM1aM2bO2 (I). The metal occupancy rate (%) of the lithium site of lithium-nickel complex oxide particles powder is obtained using Rietveld analysis of X-ray diffraction. The microcrystal size of lithium-nickel complex oxide particles powder is 700-1400 nm, which is obtained using Rietveld analysis.    x=1-1.1;    y=0-0.25 (excluding 0);    a=0-0.25 (excluding 0);    b=0-0.10;    M1=Al and/or Mn;and    M2=Zr and/or Mg.    An INDEPENDENT CLAIM is included for manufacture of lithium-nickel complex oxide particles powder, which involves preparing nickel-cobalt hydroxide particles powder by mixing nickel-cobalt hydroxide particles with sulfate aqueous solution of metallic element, ammonia aqueous solution and sodium hydroxide aqueous solution in such a way that the ammonia concentration in a reaction tank is 1.4 mol/l or less and ratio of ammonia concentration and excessive hydroxyl group concentration in reaction tank is 6 or more, mixing the obtained nickel-cobalt hydroxide particles powder with powder of lithium compound, and baking the obtained mixture.