To investigate the influence of an anti-aging agent on the properties of asphalt mixtures modified with styrene–butadiene–styrene, the surface energy parameters of a modified asphalt binder with two types of anti-aging agents and aggregates were measured using the Wilhelmy plate method and the static adsorption method. Based on the surface free energy theory, the bonding energies of the modified asphalt and aggregates were quantitatively analysed. A performance test of a modified asphalt mixture with a different anti-aging agent was then conducted. The results showed that an anti-aging agent could effectively improve the cohesive strength of an asphalt modified with styrene–butadiene–styrene, as well as the adhesive strength between the asphalt and aggregates. Additionally, an anti-humidity aging agent had a better effect on the polar component of a modified asphalt–aggregate interface, whereas an anti-ultraviolet aging agent had a better effect on the non-polar component. In addition, an anti-aging agent could significantly improve the high-temperature stability and water stability of a modified asphalt mixture. However, there was a certain degree of decrease in the low-temperature crack resistance.