A nanocomposite catalyst containing zinc oxide (ZnO), copper oxide (CuO), iron oxide (Fe3O4) and graphene was synthesized using a combined sol-gel/hydrothermal method in which we used two different types of graphene such as NGP and graphene. The as-synthesized samples were characterized by X-ray diffraction (XRD), energy dispersive X-ray (EDX), transmission electron microscopy (TEM), Fourier transform infra-red (FTIR) and vibrating sample magnetometer (VSM). We evaluated the photocatalysis, sonocatalysis, and photosonocatalysis of Fe3O4/CuO/ZnO, Fe3O4/CuOZnO/NGP and Fe3O4/CuO/ZnO/Graphene on the degradation of Methylene Blue (MB) and found that the Fe3O4/CuO/ZnO/Graphene exhibits catalytic activity higher than Fe3O4/CuO/ZnO/NGP and Fe3O4/CuO/ZnO. The effect of various scavengers has also been studied. Furthermore, all prepared nanocomposites could be used as a convenient recyclable catalyst because of their magnetic properties.