In an effort to overcome the problems of modified asphalt mixture using the typical wet process, the dry process was used to modify 70# base asphalt with the SBS/crumb rubber composite modified masterbatch. Box–Behnken response surface methodology was used to create a regression model with the interactions of five factors, which gave the optimum preparation parameters. The results show that there are many factors that have substantial influence on the laboratory performance of asphalt mixture, and the created quadratic regression model has good fitting accuracy and predictive capability. The optimum preparation parameters were an asphalt–aggregate ratio of 4.5%, modifier dosage of 2%, dry mixing time of 65 s, wet mixing time of 107 s, and mixing temperature of 189 °C. Compared to the 70# base asphalt mixture and the wet-process asphalt mixtures, the dynamic stability of the dry-process asphalt mixtures is significantly improved by 503% and 36.6%, respectively. The TSR increased by 11.4% and 4.8%, respectively, as did the residual stability by 9.6% and 2%, respectively. Compared to the 70# base asphalt mixture, the maximum flexural strain increased by 46%, though it was slightly lower under the dry process than under the traditional wet process. The results confirm the practicality of the proposed optimization strategy for the dry process.