A method for manufacturing a positive electrode active material with high charge and discharge capacity is provided. Alternatively, a method for manufacturing a positive electrode active material with high charge and discharge voltage is provided. Alternatively, a method for manufacturing a power storage device with little deterioration is provided. Alternatively, a method for manufacturing a highly safe power storage device is provided. Alternatively, a method for manufacturing a novel power storage device is provided. A method for manufacturing a secondary battery including a positive electrode active material is provided. A method for manufacturing the positive electrode active material includes a first step of synthesizing a first lithium source and a first transition metal source to form a first composite oxide; a second step of synthesizing an impurity source to provide an impurity layer for the first composite oxide after the first step; and a third step of synthesizing a second lithium source and a second transition metal source to form a second composite oxide after the second step and providing the second composite oxide over the first composite oxide provided with the impurity layer.