The stepwise hydrogenation of the C=C bond and C=O group of acrolein on Au₃ and Au₅ model systems is investigated using the density functional theory(DFT) PW91 functional. Our results show that the C=C hydrogenation is more favorable than that of C=O bond on Au₃ with the barriers of the rate-determining step being 0.35 and 0.62 eV respectively. On the other hand, the C=O reduction is preferred over the hydrogenation of the C=C bond on Au₅. The corresponding barriers of the rate-determining steps are 0.45 and 0.54 eV, respectively. This demonstrated that the second hydrogenation step controls the reaction on both Au₃ and Au₅ for C=O and C=C hydrogenation and the C=O hydrogenation on Au₅ is preferred over the hydrogenation of the C=C bond, which is helpful to address the reactivity of small size-selected supported gold clusters.