To obtain a uniform initial cord tension in an auxiliary layer of a radial tire made up of a toroidal carcass, a belt, the auxiliary layer and a tread rubber, the belt is formed by winding inextensible cords around a drum with a radius of curvature substantially the same as that of a tire tread. Further, when the belt is formed by winding the cords around a flat drum, the auxiliary layer is formed on the belt by winding a heat-shrinkable cord around the belt in spiral fashion in such a way as to apply a higher tension at both the ends of the belt layer than at the center thereof. The radial tire thus manufacture is excellent in high-speed tire durability and tire uniformity, without causing belt separation trouble at high speed.