Several versions of free-volume theory have been proposed to correlate or predict the solvent diffusion coefficient of a polymer/solvent system. The quantity of free volume is usually determined by the Williams-Landel-Ferry (WLF) equation from viscosity data of the pure component in these theories. Free volume has been extensively discussed in different equation-of-state models for a polymer. Among these models, the Simha-Someynsky (SS) hole model is the best one to describe the crystalline polymer, because it describes it very approximately close to the real structure of a crystalline polymer. In this article, we calculated the fractions of the hole free volume for several different polymers at the glass transition temperature and found that they are very close to a constant 0.025 by the SS equation of state. It is quite consistent with the value that is determined from the WLF equation. Therefore, the free volume of a crystalline polymer below the glass transition temperature (T-g) is available from the SS equation. When above the T-g, it is assumed that the volume added in thermal expansion is the only contribution of the hole free volume. Thus, a new predictive free-volume theory was proposed. The free volume of a polymer in the new predictive equation can be estimated by the SS equation of state and the thermal expansion coefficient of a polymer instead of by the viscosity of a polymer. The new predictive theory is applied to calculate the solvent self-diffusion coefficient and the solvent mutual-diffusion coefficient at different temperatures and over most of the concentration range. The results show that the predicted values are in good agreement with the experimental data in most cases.