The coordinate ring of the Grassmannian Gr(k,n) of k dimensional subspaces of \mathbb{C}^n has the structure of a cluster algebra. An additive categorification of it has been given by Jensen-King Su, using a quotient of a preprojective algebra of a cyclic quiver. This algebra is infinite dimensional and its module categories is wild in general. We show how this cluster category can be given using dimer models in the disk (certain quivers with faces) and describe the cluster categories using combinatorial tools.