Porous asphalt pavement is widely used due to its adequate water permeability, noise reduction and skid resistance. The study aims at exploring the potential of using the crumb rubber/styrene–butadienestyrene (CR/SBS) modified bitumen as high-viscosity binder for porous asphalt mixture, and investigating the effect of swelling and degradation degree of crumb rubber as well as SBS dosage on the performance of porous asphalt binder and mixture. The conventional, rheological and engineering properties of CR/SBS modified high-viscosity porous asphalt binders and mixtures were characterized. The results revealed that the CR swelling-degradation degree significantly affected the physical and viscoelastic properties of CR/SBS modified high-viscosity binders. With the swelling time prolonged, the viscosity of rubber bitumen enhanced gradually until reaching the equilibrium state, which kept falling during the degradation process dramatically. The full-swelling binders exhibited the highest complex modulus, zero-shear viscosity, rutting resistance, which deteriorated as the degradation degree increasing. However, the degradation of crumb rubber would be beneficial to improve the workability, thermal cracking resistance and deformation recovery ability of high-viscosity binder. Meanwhile, the incorporation of SBS copolymer could further strengthen both high-and-low temperatures viscoelastic performance of high-viscosity bitumen. In addition, the performance of porous asphalt with CR/SBS modified high-viscosity bitumen could meet the requirements of Marshall stability, air void content, Cantabro loss, run-off loss, anti-rutting, moisture damage resistance and permeability performance. Although the full-swelling asphalt mixture presented the best rutting resistance, it showed the poor adhesive and moisture damage resistance when compared with partial and full-degradation asphalt mixtures.