Affinity of small molecule to polymer is an essential property for designing polymer materials with tuned permeability. In the present work, we develop a computational approach to the free energy ΔG of binding a small solute molecule into polymer using the atomistic molecular dynamics (MD) simulation combined with the method of energy representation. The binding free energy ΔG is obtained by viewing a single polymer as a collection of fragments and employing an approximate functional constructed from distribution functions of the interaction energy between solute and the fragment obtained from MD simulation. The binding of water is then examined against 9 typical polymers. The relationship is addressed between the fragment size and the calculated ΔG, and a useful fragment size is identified to compromise the performance of the free-energy functional and the sampling efficiency. It is found with the appropriate fragment size that the ΔG convergence at a statistical error of ∼0.2 kcal/mol is reached at ∼4 ns of replica-exchange MD of the water-polymer system and that the mean absolute deviation of the computational ΔG from the experimental is 0.5 kcal/mol. The connection is further discussed between the polymer structure and the thermodynamic ΔG.