In this study, Fe3O4/graphene and Ag-Fe3O4/graphene composites with varying content of graphene and Ag were prepared and used as a heterogeneous Fenton catalyst for the degradation of MO and MB under UV-light irradiation. The physicochemical properties of the obtained catalysts were used for the Fenton reaction. In addition, the effects of graphene and Ag content, pH, H2O2 concentration, catalyst loading, and initial MO and MB concentrations on the degradation by the UV-Fenton process were evaluated. Results revealed that the highest removal efficiency of MO and MB is achieved at graphene and Ag concentrations of 10 and 25 wt%, respectively. Furthermore, Ag-Fe3O4/graphene composites were used to assess the degradation of a mixture of MO and MB and other anionic and cationic dyes. Results revealed that Ag-Fe3O4/graphene composites can be used as a broad-spectrum catalyst with good efficiency for the removal of several dye contaminants in water. Moreover, the effect of the addition of ascorbic acid (AA) on dye degradation was investigated. AA accelerated the degradation of organic dyes compared to that without AA. The obtained results revealed that Ag-Fe3O4/graphene composites exhibit stable catalytic activity and reusability after four successive runs.