Cellulase enzymes often contain carbohydrate-binding modules (CBMs) for binding to cellulose. The mechanisms by which CBMs recognize specific surfaces of cellulose and aid in deconstruction are essential to understand cellulase action. The Family 1 CBM from the Trichoderma reesei Family 7 cellobiohydrolase, Cel7A, is known to selectively bind to hydrophobic surfaces of native cellulose. It is most commonly suggested that three aromatic residues identify the planar binding face of this CBM, but several recent studies have challenged this hypothesis. Here, we use molecular simulation to study the CBM binding orientation and affinity on hydrophilic and hydrophobic cellulose surfaces. Roughly 43 μs of molecular dynamics simulations were conducted, which enables statistically significant observations. We quantify the fractions of the CBMs that detach from crystal surfaces or diffuse to other surfaces, the diffusivity along the hydrophobic surface, and the overall orientation of the CBM on both hydrophobic and hydrophilic faces. The simulations demonstrate that there is a thermodynamic driving force for the Cel7A CBM to bind preferentially to the hydrophobic surface of cellulose relative to hydrophilic surfaces. In addition, the simulations demonstrate that the CBM can diffuse from hydrophilic surfaces to the hydrophobic surface, whereas the reverse transition is not observed. Lastly, our simulations suggest that the flat faces of Family 1 CBMs are the preferred binding surfaces. These results enhance our understanding of how Family 1 CBMs interact with and recognize specific cellulose surfaces and provide insights into the initial events of cellulase adsorption and diffusion on cellulose.