A tire reinforcing member winding apparatus having a rotary building drum; winding guides provided upstream to the drum so as to be moved along the axis of the drum while guiding belt-like tire reinforcing members supplied to the drum, to spirally wind the tire reinforcing members on the drum; tensile force application means for applying tensile forces to the tire reinforcing members; detection means for detecting the positions of the tire reinforcing members in the axial direction of the drum; and a control means by which the tensile forces applied to the tire reinforcing members by the tensile force application means are changed depending on the results of the detection by the detection means, so that the tensile forces of the tire reinforcing members wound on the drum are made higher far from the axially central portion of the drum than near the axially central portion.