The assembly of small water clusters (H2O)n, n = 1-6, on a graphite surface is studied using a density functional tight-binding method complemented with an empirical van der Waals force correction, with confirmation using second-order Møller-Plesset perturbation theory. It is shown that the optimized geometry of the water hexamer may change its original structure to an isoenergy one when interacting with a graphite surface in some specific orientation, while the smaller water cluster will maintain its cyclic or linear configurations (for the water dimer). The binding energy of water clusters interacting with graphite is dependent on the number of water molecules that form hydrogen bonds, but is independent of the water cluster size. These physically adsorbed water clusters show little change in their IR peak position and leave an almost perfect graphite surface.