The interaction of Cu-n(n = 1-4) cluster with the dehydrated gamma-Al2O3(110), hydrated gamma-Al2O3(110) and dehydrated gamma-Al2O3(100) surfaces has been systematically investigated to illustrate the influence of the hydroxylation of gamma-Al2O3 surfaces on the stability and growth of Cu for Cu/gamma-Al2O3 catalyst. Here, we present the main results obtained by the density functional theory together with slab model calculations. Our results show that the adsorption of Cu-n(n = 2-4) cluster on the gamma-Al2O3(110) surface is more stable than that on the gamma-Al2O3(100) surface, for the single Cu atom, the reverse becomes true. For the gamma-Al2O3(110) surface, the adsorption of Cu-n(n = 2-4) cluster on the dehydrated surface is more stable than that on the hydrated surface due to the presence of the surface hydroxyls, however, the adsorption of the single Cu atom on the hydrated surface is more stable than that on the dehydrated surface due to the larger Cu-support interaction energy. On the other hand, compared to the gamma-Al2O3(100) surface, the gamma-Al2O3(110) surface is more favorable for the growth of Cu-n clusters, in which the presence of surface hydroxyls reduces the growth ability of Cu-n clusters. (c) 2013 Elsevier B.V. All rights reserved.