Au@Cu2O core-shell nanocomposites (NCs) were synthesized by reducing copper nitrate on Au colloids with hydrazine. The thickness of the Cu2O shells could be varied by adjusting the molar ratios of Au: Cu. The results showed that the thickness of Cu2O shells played a crucial role in the catalytic activity of Au@Cu2O NCs under dark condition. The Au@Cu2O-Ag ternary NCs were further prepared by a simple galvanic replacement reaction method. Moreover, the surface features were revealed by TEM, XRD, XPS, and UV–Vis techniques. Compared with Au@Cu2O NCs, the ternary Au@Cu2O-Ag NCs had an excellent catalytic performance. The degradation of methyl orange (MO) catalyzed by Au@Cu2O-Ag NCs was achieved within 4 min. The mechanism study proved that the synergistic effects of Au@Cu2O-Ag NCs and sodium borohydride facilitated the degradation of MO. Hence, the designed Au@Cu2O-Ag NCs with high catalytic efficiency and good stability are expected to be the ideal environmental nanocatalysts for the degradation of dye pollutants in wastewater.