It is an object to provide a manufacturing method for a large amount of positive electrode active material with few variations, having a highly uniform surface condition, micro-size, and high performance. An aqueous solution of a compound, which becomes the source material for the positive electrode active material, is put in an airtight container and irradiated with microwaves, thus heating while water in the airtight container is evaporated and a high pressure is formed in the air tight container. A large amount of micro-sized positive electrode active material having a highly uniform surface condition can be formed. A compound, which becomes the source material for the positive electrode active material, is put in an airtight container and irradiated with microwaves, thus heating while water in the airtight container is evaporated and a high pressure is formed in the air tight container.