Solubility parameters play an important role in predicting compatibility between components. The current study on solubility parameters of carbon materials (graphene, carbon nanotubes, and fullerene, etc.) is unsatisfactory and stagnant due to experimental limitations, especially the lack of a quantitative relationship between functional groups and solubility parameters. Fundamental understanding of the high-performance nanocomposites obtained by carbon material modification is scarce. Therefore, in the past, the trial and error method was often used for the modification of carbon materials, and no theory has been formed to guide the experiment. In this work, the effect of defects, size, and the number of walls on the Hildebrand solubility parameter (delta(T)) of carbon nanotubes (CNTs) was investigated by molecular dynamics (MD) simulation. Besides, three-component Hansen solubility parameters (delta(D) , delta(p), delta(H)) were transformed into two-component solubility parameters (delta(vdw ), delta(elec)). The quantitative relation between functional groups and two-component solubility parameters of single-walled carbon nanotubes (SWCNTs) was then given. An important finding is that the delta(T) and delta(vdw) of SWCNTs first decrease, reach a minimum, and then increase with increasing grafting ratio. The thermodynamic compatibility between functionalized SWCNTs and six typical polymers was investigated by the Flory-Huggins mixing model. Two-component solubility parameters were proven to be able to effectively predict their compatibility. Importantly, we theoretically gave the optimum grafting ratio at which the compatibility between functionalized SWCNTs and polymers is the best. The functionalization principle of SWCNTs toward good compatibility between SWCNTs and polymers was also given. This study gives a new insight into the solubility parameters of functionalized SWCNTs and provides theoretical guidance for the preparation of high-performance SWCNTs/polymers composites.