The main distresses of asphalt pavements in seasonally frozen regions are due to the effects of water action, freeze-thaw cycles, and so on. Basalt fiber, as an eco-friendly mineral fiber with high mechanical performance, has been adopted to reinforce asphalt mixture in order to improve its mechanical properties. This study investigated the freeze-thaw damage characteristics of asphalt mixtures reinforced with eco-friendly basalt fiber by volume and mechanical properties—air voids, splitting tensile strength, and indirect tensile stiffness modulus tests. Test results indicated that asphalt mixtures reinforced with eco-friendly basalt fiber had better mechanical properties (i.e., splitting tensile strength and indirect tensile stiffness modulus) before and after freeze-thaw cycles. Furthermore, this study developed logistic damage models of asphalt mixtures in terms of the damage characteristics, and found that adding basalt fiber could significantly reduce the damage degree by about 25%, and slow down the damage grow rate by about 45% compared with control group without basalt fiber. Moreover, multi-variable grey models (GM) (1,N) were established for modelling the damage characteristics of asphalt mixtures under the effect of freeze-thaw cycles. GM (1,3) was proven as an effective prediction model to perform better in prediction accuracy compared to GM (1,2).