A critical role of the Family 7 cellobiohydrolase (Cel7A) carbohydrate binding domain (CBD) is to bind to a cellulose surface and increase the enzyme concentration on the surface. Several residues of Trichoderma reesei Cel7A CBD, including Y5, N29, Y31, Y32 and Q34, contribute to cellulose binding, as revealed by early experimental studies. To investigate the interactions between these important residues and cellulose, we applied a thermodynamic integration method to calculate the cellulose-Cel7A CBD binding free energy changes caused by Y5A, N29A, Y31A, Y32A and Q34A mutations. The experimental binding trend was successfully predicted, proving the effectiveness of the complex model. For the two polar residue mutants N29A and Q34A, the changes in the electrostatics are comparable to those of van der Waals, while for three Y to A mutants, the free energy differences mainly come from van der Waals interactions. However, in both cases, the electrostatics dominates the interactions between individual residues and cellulose. The side chains of these residues are rigidified after the complex is formed. The binding free energy changes for the two mutants Y5W and Y31W were also determined, and for these the van der Waals interaction was strengthened but the electrostatics was weakened.