In an apparatus for affixing a tire component member, a capacity of a driving means for a traveling head is decreased, and start end positions of affixing the tire component member are aligned in a peripheral direction of a drum and a widthwise overlap amount between the tire component members is made constant as is expected, and also a cycle time is shortened, in which the apparatus comprises a traveling head 2 moving forward and rearward in an axial direction of a drum 1, a clamp means 9 pushing a front end portion of the tire component member 3 protruded ahead from the traveling head 2 onto the peripheral face of the drum, a cutting means 12 arranged at one end side of the drum apart from the clamp means 9, guide rolls 5 arranged on the traveling head 2 and specifying a widthwise position of the tire component member 3, and a chuck means pulling the tire component member 3 to the clamp means 9.