The main objective of this research is to determine the effect of crumb rubber on the creep stiffness and permanent deformation of asphalt concrete mixtures. Rubber was used as an additive to the base bitumen (by weight of bitumen in total mix) at four contents: (0, 7, 10, and 13%) by volume of binder. Then, they were exposed to creep test through the consolidation-testing machine. It was found that, the use of crumb rubber decreases the economic cost of asphalt mixture constructing and it was also found that The addition of crumb rubber modifier by 10% (by weight of bitumen in total mix) was the optimum content of CRM to achieve the best improvement for the modified mixtures properties and performance of asphalt concrete mixtures by reducing rutting (Permanent deformation).