Composite nanostructure materials are widely used in catalysis. They exhibit several characteristics, such as the unique structural advantage and the synergism among their components, which significantly enhances their catalytic performance. In this work, CoPt nanoparticles and reduced-graphene-oxide-based nanocomposite catalysts (rGO/CoPt, rGO/CoPt/Ag) were prepared by using a facile co-reduction strategy. The crystalline structure, morphology, composition, and optical characteristics of the CoPt nanoparticles, rGO/CoPt nanocomposite, and rGO/CoPt/Ag nanocomposite catalysts were investigated by a set of techniques. The ID/IG value of the rGO/CoPt/Ag nanocomposite is 1.158, higher than that of rGO/CoPt (1.042). The kinetic apparent rate constant, k, of the rGO/CoPt/Ag nanocomposite against 4-nitrophenol (4-NP) reduction is 5.306 min−1, which is higher than that of CoPt (0.495 min−1) and rGO/CoPt (1.283 min−1). The normalized rate constant, knor, of the rGO/CoPt/Ag nanocomposite is 56.76 min−1mg−1, which is higher than some other catalytic materials. The rGO/CoPt/Ag nanocomposite shows a significantly enhanced catalytic performance when compared to CoPt nanoparticles and the rGO/CoPt nanocomposite, which may confirm that the novel rGO/CoPt/Ag nanocomposite is a promising catalyst for the application of catalytic fields.