Controlling the electronic structure and surface strain of a nanoparticle catalyst has become an important strategy to tune and to optimize its catalytic efficiency for a chemical reaction. Using density functional theory (DFT) calculations, we predicted that core/shell M/CuPd (M = Ag, Au) NPs with a 0.8 or 1.2 nm CuPd2 shell have similar but optimal surface strain and composition and may surpass Pt in catalyzing oxygen reduction reactions. We synthesized monodisperse M/CuPd NPs by the coreduction of palladium acetylacetonate and copper acetylacetonate in the presence of Ag (or Au) nanoparticles with controlled shell thicknesses of 0.4, 0.75, and 1.1 nm and CuPd compositions and evaluated their catalysis for the oxygen reduction reaction in 0.1 M KOH solution. As predicted, our Ag/Cu37Pd63 and Au/Cu40Pd60 catalysts with 0.75 and 1.1 nm shells were more efficient catalysts than the commercial Pt catalyst (Fuel Cells Store), with their mass activity reaching 0.20 A/mg of noble metal at -0.1 V vs Ag/AgCl (4M KCl); this was over 3 times higher than that (0.06 A/mg Pt) from the commercial Pt. These Ag(Au)/CuPd nanoparticles are promising non-Pt catalysts for oxygen reduction reactions.