The interaction of H2O molecules with the CeO2(1 1 1) and (1 1 0) surfaces with the supported Au and Pd single atom catalysts (Au/CeO2 and Pd/CeO2) has been studied based on the first-principles calculation. It is found that H2O energetically prefers to be dissociative adsorption on the Pd/CeO2(1 1 0), Au/CeO2(1 1 1) and Au/CeO2(1 1 0) surfaces with the adsorption energies of 1.71, 1.91 and 1.40 eV, respectively, while both molecular (1.06 eV) and dissociative adsorption (1.15 eV) may coexist for H2O on the Pd/CeO2(1 1 1) surface. H2O dissociative adsorption is much more exothermic on the Pd/CeO2(1 1 0) surface than on the Pd/CeO2(1 1 1) surface, while the opposite behavior has been observed for H2O adsorption on the Au/CeO2 surface. The relevant mechanism has been discussed based on the electronic structure analysis. In addition, we have made a comparison between the Pd(Au)/CeO2 surfaces and the pristine CeO2 surfaces in terms of the H2O adsorption exothermicity and the kinetic barrier of H2O dissociation, which indicate that the supported metal single atoms can greatly enhance the chemical activity of CeO2 toward H2O. Our study would give useful insights into the reactions involving H2O catalyzed by the CeO2-supported Pd and Au nanocatalysts, when the Pd and Au are existing in the form of single atoms.