NOVELTY - A positive electrode active material manufacturing method involves mixing an aqueous solution aqA containing a metallic element MT and additional element EA, and aqueous solution aqB containing additional element EB (S140). Hydroxide containing the MT, the EA and the EB is produced. The hydroxide and a lithium compound are mixed (S170). The mixture is baked (S180) to produce the lithium transition metal oxide. The aqA and aqB solutions are mixed and the hydroxide is deposited on alkaline conditions. The hydroxide growing is performed (S150) by maintaining the mixed solution to the alkalinity.    USE - Method for manufacturing a positive electrode active material that is utilized in a lithium secondary battery as a driving power supply for a vehicle (all claimed) such as hybrid vehicle, plug-in hybrid motor vehicle or electric vehicle, a personal computer and a portable terminal.    ADVANTAGE - The method enables improving charging/discharging efficiency, capacity, output characteristics, energy density, thermal stability and durability of the battery.    DETAILED DESCRIPTION - A positive electrode active material manufacturing method involves mixing an aqueous solution aqA containing a metallic element MT and additional element EA, and aqueous solution aqB containing additional element EB, where the MT is nickel, cobalt and/or manganese, and the hollow structure of the material has a shell part and a hollow part. Hydroxide containing the MT, the EA and the EB is produced. The hydroxide and a lithium compound are mixed. The mixture is baked to produce the lithium transition metal oxide. The aqA and aqB solutions are mixed and the hydroxide is deposited on alkaline conditions. The hydroxide growing is performed by maintaining the mixed solution to the alkalinity. An INDEPENDENT CLAIM is also included for a positive electrode active material.    DESCRIPTION OF DRAWING(S) - The drawing shows a flowchart illustrating a method for manufacturing a positive electrode active material. '(Drawing includes non-English language text)'    Step for mixing aqA containing MT and EA, and aqB containing EB (S140)    Step for performing hydroxide growing (S150)    Step for mixing hydroxide and lithium compound (S170)    Step for baking the mixture (S180)