With the increase in highway traffic volume, many waste tires are being produced, which puts serious pressure on the global ecological environment. Processing waste tires into powder and adding them to asphalt is an important and effective way to solve this noticeable environmental challenge. In this paper, to produce ground tire rubber (GTR) and styrene-butadiene-styrene (SBS) compound-modified asphalt, GTR was put into SBS-modified asphalt (GTRSA). Subsequently, some ordinary property tests, frequency sweep tests, and multiple stress creep recovery tests were conducted to investigate the conventional properties and rheological properties of GTRSA. Moreover, the 2S2P1D (two springs, two parabolic elements, and one dashpot) model was adopted to analyze the consequences of adding GTR content on the rheological properties of GTRSA. Finally, the Pearson correlation coefficient was employed to reveal the connection between the conventional properties and the rheological properties. The results show that GTR has a great impact on improving the rutting resistance, thermo-sensitive performance, shear resistance capability, stress sensitivity, and creep recovery performance of GTRSA. Adding 20% GTR can improve the creep recovery rate to 80.8%. The 5 °C ductility index suggests that GTR makes a difference to the low-temperature properties. The rheological properties and conventional properties had a strong linear link.