Silica-alumina (SiO2-Al2O3)-supported palladium catalysts prepared by adsorption of the tetrachloropalladate anion (PdCl42−) followed by calcination and reduction with either hexanol or hydrogen were studied for the aerobic oxidation of alcohols. The mean size of the Pd particles over the SiO2-Al2O3 support was found to depend on the Si/Al ratio, and a decrease in the Si/Al ratio resulted in a decrease in the mean size of the Pd nanoparticles. By changing the Si/Al ratio, we obtained supported Pd nanoparticles with mean sizes ranging from 2.2 to 10 nm. The interaction between the Pd precursor and the support was proposed to play a key role in tuning the mean size of the Pd nanoparticles. The Pd/SiO2-Al2O3 catalyst with an appropriate mean size of Pd particles could catalyze the aerobic oxidation of various alcohols to the corresponding carbonyl compounds, and this catalyst was particularly efficient for the solvent-free conversion of benzyl alcohol. The intrinsic turnover frequency per surface Pd atom depended significantly on the mean size of Pd particles and showed a maximum at a medium mean size (3.6–4.3 nm), revealing that the aerobic oxidation of benzyl alcohol catalyzed by the supported Pd nanoparticles was structure-sensitive.