During manufacturing of a tire component that includes a process of adhering a sheet-like rubber member 8b that is held by a supply section 30 to a drum 22, positions of ends 7d1, 7d2 n a width direction of the sheet-like rubber member 8b are detected by using sensors 52, 54 provided between the supply section 30 and the drum 22, and the supply section 30 is moved in a width direction X of the sheet-like rubber member 8b in accordance with the detected positions, so as to adhere the sheet-like rubber member 8b to a specified position on the drum 22.