The interfacial adhesion between asphalt binder and carbon nanotubes (CNTs) depends on many nanoscopic properties such as diffusion of SARA molecules on CNTs surface. Functionalization of CNTs with Oxygens (O=CNTs), hydroxyl groups (HO–CNTs), and hydrogens (H–CNTs) has been an effective way to modify the surface properties of CNTs and ultimately the macroscopic properties of the CNT-composites. This paper presents the effect of different dosages of oxygenated and hydrogenated CNTs on the adhesion and diffusion of SARA molecules on CNTs’ surfaces. First, reactive molecular dynamics simulation is used to oxygenate and hydrogenate CNTs up to a certain dosage. Next, it is employed to model the interaction and diffusion of SARA molecules with the functionalized CNTs. We employ the steer molecular dynamic (SMD) and Einstein formula to calculate the adhesion and diffusion properties. The results demonstrate that hydrogenation has little effect on the adhesion energy, while oxygenation can increase adhesion energy up to 100% for 25% dosage. The diffusion coefficient dramatically drops for both oxygenated and hydrogenated CNTs, with lower values for the latter. We observe that for hydrogenated and oxygenated CNTs at different dosages, asphaltene, resin, aromatic, and saturate molecules have the highest to lowest values, respectively.