The invention discloses an epoxy-terminated polysulfide rubber modified SBS, a preparation method thereof, and an application of the modified SBS in modified asphalt. The preparation method of the modified SBS comprises the following steps: performing anionic polymerization to obtain a styrene-butadiene block copolymer sol containing active terminal lithium, and coupling the styrene-butadiene block copolymer sol with an epoxy-terminated polysulfide rubber to obtain the epoxy-terminated polysulfide rubber modified styrene-butadiene block copolymer. The polymer retains the original mechanical properties of the styrene-butadiene block polymer, makes the polysulfide rubber have low-temperature flexibility, weather resistance and aging resistance, and improves the polarity of the butadiene-styrene block polymer, so the modified SBS has an improved plasticizing effect and enhanced affinity, and can obviously reduce the segregation phenomenon of the butadiene-styrene block polymer and asphaltwhen used for asphalt modification.