NOVELTY - An active material comprises alpha -sodium iron oxide type crystal structure, and average composition comprising a transition metal (Me) containing cobalt, nickel, and manganese and lithium-transition metal composite oxide, where the lithium-transition metal composite oxides are particle, which have a core and a coated part, the coated part has nickel concentration more than the nickel concentration of the core, and manganese concentration less than the manganese concentration of the core.    USE - Active material for use in electrode of non-aqueous electrolyte secondary battery that is utilized in electrical storage apparatus (all claimed), power supply for electronic devices, electric power storage and electronic vehicle such as motor vehicles, such as an electric vehicle, hybrid vehicle and a plug-in hybrid motor vehicle.    ADVANTAGE - The material has improved electronic conductivity and coatability, improves energy density, charging/discharging cycle performance, output performance of the battery.    DETAILED DESCRIPTION - An active material comprises alpha -sodium iron oxide type crystal structure, average composition comprising a transition metal (Me) containing cobalt, nickel, and manganese and lithium-transition metal composite oxide according to the molar ratio of lithium to transition metal (Me) of more than 1, where the transition metal (Me) has mass ratio of lithium to average composition comprising cobalt, nickel, and manganese is more than 1, the lithium- transition metal composite oxides are particle, which have a core and a coated part, the coated part has nickel concentration more than the nickel concentration of the core, and manganese concentration less than the manganese concentration of the core, the coated part has a gradient of nickel concentration, When the center position of the particle is set t o zero, and a surface position to 1, and starting point X of a nickel concentration gradient is more than 0.5, but less than 1.0. An INDEPENDENT CLAIM is also included for a method for manufacturing an active material.