NOVELTY - A positive-electrode active material comprises composite oxide (I) having a lamellar structure with a stacking fault density of 0.4 or less. The average primary particle diameter of the composite oxide is 150 nm or less. The ratio of the diffraction peak intensity around angle (2( theta )) of 20.8 degrees to the diffraction peak intensity round angle (2( theta )) of 18.6 degrees is 0.5 or less, based on X-ray diffraction pattern.    USE - Active material is used for material for positive electrode of nonaqueous electrolyte secondary battery (all claimed) for electric vehicle and hybrid vehicle.    ADVANTAGE - The positive-electrode active material provides nonaqueous electrolyte secondary battery having high capacity and excellent load characteristics.    DETAILED DESCRIPTION - A positive-electrode active material comprises composite oxide of formula: Li(LiaMnbMe'c)O2-d (I) (where Me' is element chosen from transition metals (excluding manganese), a is more than 0 and less than 1/3, b is more than 0 and less than 2/3, c is more than 0 and less than 1 and d is 0-0.2) having a lamellar structure. The average primary particle diameter of the composite oxide is 150 nm or less. The ratio (I(020)/I(003)) of the diffraction peak intensity (I(020)) around angle (2( theta )) of 20.8 degrees to the diffraction peak intensity (I(003)) around angle (2( theta )) of 18.6 degrees is 0.5 or less, based on X-ray diffraction pattern. The lamellar structure has a stacking fault density of 0.4 or less. INDEPENDENT CLAIMS are included for the following:    (1) positive electrode material, which contains the positive-electrode active material, a conductive support agent and a binder;    (2) positive electrode;    (3) nonaqueous electrolyte secondary battery; and    (4) manufacture of positive-electrode active material, which involves using a mixture of manganese compound particles having average primary particle diameter of 5-120 nm, transition metal salt and lithium salt, or mixture of precursor oxide particles containing manganese and transition metals (Me') and having average primary particle diameter of 5-120 nm, and/or precursor hydroxide particles, and lithium salt.