Asphalt mixture is susceptible to moisture damage under the effect of freeze-thaw (F-T) cycles. In this paper, crumb rubber (CR) was used to modify stone mastic asphalt (SMA) and the effects of diatomite and styrene butadiene styrene (SBS) on antifreezing performances of crumb rubber modified SMA (CRSMA) were investigated. Regression analysis and modified grey model (MGM) were used to construct the prediction models for properties of modified mixtures. CRSMA, CR and diatomite modified SMA (CRDSMA), and CR and SBS modified SMA (CRSSMA) were prepared in laboratory, respectively. Process of F-T cycles was designed. Air void, indirect tensile strength (ITS), and indirect tensile stiffness modulus (ITSM) were measured to evaluate the antifreezing performances of CRSMA, CRDSMA, and CRSSMA. Results indicate that air voids increase with the increasing of F-T cycles. ITS and ITSM all decrease with the increasing of F-T cycles. The addition of diatomite and SBS can reduce the air void and improve the ITS and ITSM of CRSMA. CRSSMA presents the lowest air void, highest tensile strength, and largest stiffness modulus, which reveals that CRSSMA has the best F-T resistance among three different kinds of mixtures. Moreover, MGM (1, 2) models present more favorable accuracy in prediction of air void and ITS compared with regression ones.