In order to improve the high-temperature performance, antiaging performance, and storage stability of rubber asphalt, nano-organic montmorillonite (NOMMT) was mixed with rubber asphalt. Macroscopic influences of NOMMT on rubber asphalt were measured through penetration, softening point, ductility, rotational viscosity tests, dynamic shear rheology test, and bending beam rheology test at low temperature and were conducted on rubber asphalt with different contents of NOMMT. Then, the microscopic mechanism of NOMMT on the microscopic performance of rubber asphalt was studied through using scanning electron microscopy (SEM), infrared spectroscopy (IR), and differential scanning calorimetry (DSC). The results showed that the rubber particles were smoother, uniform, and dispersed after NOMMT was introduced, and the compatibility between NOMMT and crumbed rubber powder was good. Some stable structures were formed in the composite modified asphalt. The disappearance of alcohol phenol and the increase in related groups such as alkane, benzene, and hydrocarbon indicated that chemical reaction occurred between NOMMT and rubber asphalt, resulting in the changes of the performance of the composite modified system, so that high-temperature stability, antiaging properties, and storage stability were improved but its low-temperature performance was decreased.