Based on the four-component theory of asphalt, molecular models of the saturate, aromatic, resin, and asphaltene were constructed, respectively. The styrene–butadiene–styrene (SBS) polymer was used as the modifier. Using density functional theory (DFT) to study the effect of SBS on the molecular vibration of each component of asphalt, the vibration spectrums and binding energy of the systems composed of SBS and each component molecule of asphalt were calculated. Prepared SBS modified asphalt and measured Fourier transform infrared spectroscopy (FTIR) before and after the experiment. The results show that after SBS was added to asphalt, no chemical reaction occurred, and the system was mainly physical blending. The vibrational peak intensity of SBS and the light components of asphalt (saturate and aromatic) is stronger than that of SBS and the heavy components of asphalt (resin and asphaltene). The interaction strengths of asphalt components and polybutadiene (PB) blocks, polystyrene (PS) blocks of SBS are different. The binding energy of SBS and the saturate is the lowest and the bonding of the system is weakest. The bonding of the systems of SBS and the aromatic, resin, asphaltene is stable, and the stability of these systems are all stronger than that of SBS and the saturate.