A coarse-grained model for the simulation of cellulose 1β was derived, in which each β-D-glucose unit is represented by three beads. The bonded interactions are derived from atomistic simulation of crystalline cellulose 1β in water, whereas the non-bonded interactions are based on modification of an existing coarse-grained model for malto-oligosaccharides to incorporate directionality into this model. When used to study the interaction of the family 1 carbohydrate-binding module (CBM1) with this cellulose surface model, the CBM “opens” as in earlier atomistic simulations. Furthermore, this cellulose 1β model produces simulations in which the CBM translates along a broken cellodextrin chain. This processive motion of CBH I has long been suggested by experimental studies, but has never before been observed in computer simulations.