The surface structure sensitivity of the water-gas shift (WGS) reaction (CO + H2O --> CO2 + H-2) over the Cu(111), Cu(100), and Cu(110) surfaces has been studied by first-principles density functional calculations together with the UBI-QEP approach. The Cu(hkl) surfaces are simulated by the Cu-10 and Cu-14 cluster models. The selectivity of the WGS reaction on the well-defined single-crystal surfaces is closely associated with the differences in the dissociation energies of H2O on the metal surfaces. The trend in the calculated dissociation energies and activation barriers follows the order Cu(110) < Cu(100) < Cu(111), suggesting that the most efficient crystal surface for catalyzing the WGS reaction is Cu(110), closely followed by the Cu(100) surface, and that the more densely packed Cu(111) surface is the least active among the Cu(hkl) surfaces studied here. The present calculations are in good agreement with experimental observations.