A pneumatic radial tire includes a belt arranged on the radially outer side of a carcass, and a band arranged on the radially outer side of the belt and composed of one or more continuous organic fiber cords wound spirally and approximately parallel to the circumferential direction of the tire. A radial tire manufacturing method includes the steps of laminating a predetermined number of belt plies on a belt drum or belt ring for forming a belt, and winding one to several organic fiber cords continuously and spirally in the circumferential direction of the belt on the outer surface of the formed belt in order to form a band. A band forming device includes a device for drawing out a cord to be wound, a device for traversing a let-off device in the widthwise direction of the belt, and a device for controlling the traverse of the let-off device. A method of forming belt-band-tread rubber assemblies includes a step of expanding the diameter of the belt drum so that the shape in axial section of belt drum becomes approximately the same as the finished shape of the band in the vulcanization mold. An assembly forming device includes a diameter-variable belt drum, wherein the shape in the axial section of the circumferential surface of the annular body in the diameter-expanded state is the same as or similar to the finished shaped of the band in a mold.