NOVELTY - Lithium metal complex oxide has layered structure and specific composition (I). The lithium metal complex oxide has volume-based particle size distribution of 4-20 mu m, measured by laser diffraction-scattering type particle size distribution, and secondary particle area which is measured by measuring the magnitude of secondary particles with respect to volume-based particle size distribution. The ratio of primary-particle area and secondary particle area is 0.004-0.035.    USE - Lithium metal complex oxide is used as positive electrode active material for lithium secondary battery for hybrid electric vehicle and electric vehicle (all claimed). Uses include but are not limited to video camera, notebook personal computer and mobile telephone.    ADVANTAGE - The lithium secondary battery comprising lithium metal complex oxide has excellent cycling characteristics, charging/discharging characteristics and slurry characteristics.    DETAILED DESCRIPTION - Lithium metal complex oxide has layered structure and compositional formula: Li1+xM1-xO2. The lithium metal complex oxide has volume-based particle size distribution (D50) of 4-20 mu m, measured by laser diffraction-scattering type particle size distribution, and secondary particle area which is measured by measuring the magnitude of secondary particles with respect to D50. The ratio of primary-particle area and secondary particle area is 0.004-0.035. The minimum value of the powder compressive strength of the lithium metal complex oxide is measured by crushing powder under more than 70 MPa using a micro compression tester. The secondary particle area is measured by observing lithium metal complex oxide with an electron microscope, selecting five secondary particles having magnitude with respect to D50 randomly, measuring area of secondary particles by making the length of the particles into a diameter in spherical case in which the secondary particles are amorphous the area is measured by resembling the spherical form, and averaging the area. The primary particle area is measured by observing lithium metal complex oxide with an electron microscope, and selecting five secondary particles randomly in which ten-pieces of primary particles are selected. When the primary particles are rod-shape, an area is measured by longest portion of grain-boundary space along longer axis and breadth of grain-boundary space. The area of primary particles is measured by making length of the grain-boundary space into diameter in spherical case. The average area of 50-pieces is measured as primary particle area.    M=Mn, Co, Ni, or transition element chosen from group 3-11 elements and element of 3rd period of periodic table.    N.B. x is not defined. INDEPENDENT CLAIMS are included for the following:    (1) lithium secondary battery, which is equipped with lithium metal complex oxide as a positive electrode active material; and    (2) hybrid electric vehicle, which is equipped with lithium secondary battery.