Storage-stable styrene-butadiene-styrene triblock copolymer (SBS)-modified asphalt was prepared by dynamic vulcanization. The vulcanization characteristics of the asphalt/SBS/sulfur blend were studied using a strain-controlled rheometer. The vulcanization of SBS in the asphalt resulted in a marked increase in the torque of the blend. In addition, the vulcanization of a butadiene rubber (BR)/sulfur blend was significantly influenced by the addition of asphalt through a curemeter. The existence of asphalt can accelerate the vulcanization of BR/sulfur blend and reduce its reversion. The preparation process of storage-stable SBS-modified asphalt by dynamic vulcanization was identified by a plot of the electric current versus time. The addition of sulfur to the SBS-modified asphalts resulted in the formation of chemically vulcanized network structures in the modified binders. The physical properties of the SBS-modified asphalt containing sulfur were compared to those of the modified binders without sulfur. The storage stability of the SBS-modified asphalt was effectively improved by the addition of sulfur. The rheological properties of the SBS-modified asphalts before and after adding sulfur were characterized by using dynamic shear rheometry and a rotational viscometer. As indicated by the monitored morphology, the compatibility and high-temperature storage stability of SBS-modified asphalts were improved by the addition of sulfur.