Acrylamide with a double bond and amide group can not only copolymerize with macromolecules of crumb rubber but also react with acidic groups in asphalt, so it was selected as a modifier to activate crumb rubber through chemical graft action. The purpose is to improve the compatibility between crumb rubber and asphalt and thus improve the rheological properties and storage stability of rubber asphalt. Infrared spectroscopy (IR) and scanning electron microscopy (SEM) were used to characterize the crumb rubbers and their modified asphalt. It was found that the crumb rubber of grafting acrylamide had better compatibility in asphalt due to its larger specific surface area and chemical reaction with asphalt. In addition, the high temperature rheological test, low temperature creep test, and polymer separation test were carried out to study the effect of grafted activated crumb rubber on the properties of modified asphalt. The results showed that compared with modified asphalt with common crumb rubber (CRMA), the rheological properties and storage stability of modified asphalt with grafting activated crumb rubber (A–G–R) were improved significantly. The results of microscopic and macroscopic tests show that the activated rubber particles have a larger contact area with asphalt due to a rougher surface and the chemical cross-linking between rubber particles and asphalt further strengthens their interaction. Therefore, there is a relatively stable blend system formed in modified asphalt, and its performance of modified asphalt has been improved.