NOVELTY - A positive electrode active material comprises lithium-transition metal composite oxide having ( alpha )-sodium-iron oxide structure and pore volume of 0.055-0.08 cm3/g or more in pore region having pore diameter of 60 nm or less which shows maximum value of differential pore volume calculated by BJH method from adsorption isotherm using nitrogen gas adsorption method. The molar ratio of lithium with respect to transition metal including cobalt, nickel and manganese in the composite oxide, is 1.2-1.6. The composite oxide exhibits single phase which belongs to space group R3-m at 1000 degrees C.    USE - Active material is used for positive electrode for lithium secondary battery (all claimed) for hybrid vehicle, electric vehicle and plug-in hybrid motor vehicle.    ADVANTAGE - The lithium secondary battery containing the positive electrode active material has excellent initial stage efficiency and high discharge performance.    DETAILED DESCRIPTION - A positive electrode active material comprises lithium-transition metal composite oxide having ( alpha )-sodium-iron oxide (NaFeO2) structure and pore volume of 0.055-0.08 cm3/g or more in pore region having pore diameter of 60 nm or less which shows maximum value of differential pore volume calculated by BJH method from adsorption isotherm using nitrogen gas adsorption method. The molar ratio of lithium with respect to transition metal including cobalt, nickel and manganese in the composite oxide, is 1.2-1.6. The composite oxide exhibits single phase which belongs to space group R3-m at 1000 degrees C. An INDEPENDENT CLAIM is included for manufacture of positive electrode active material, which involves producing precursor containing cobalt, nickel and manganese as transition metal, mixing the precursor and lithium salt, baking at 800 degrees C or more to produce lithium-transition metal composite oxide, and treating the oxide using acid.    DESCRIPTION OF DRAWING(S) - The drawing shows a perspective view of lithium secondary battery containing the positive electrode active material.    Lithium secondary battery (1)    Electrode group (2)    Battery container (3)    Positive electrode terminal (4)    Negative electrode terminal (5)