Metal/metal oxide nanostructures based reduced graphene oxide (LrGO-Ag, LrGO-Cu2O, LrGO-Ag-Cu2O) nanocomposites were obtained via green method using Cetraria islandica (L.) Ach. lichen extract. Fourier transform infrared (FTIR) spectroscopy, transmission electron microscopy (TEM), scanning electron microscope energy-dispersive X-ray spectroscopy (SEM-EDX), ultraviolet-visible (UV-Vis) spectroscopy, X-ray diffraction (XRD) and X-ray photo-electron spectroscopy (XPS) were performed to analyze the prepared nanostructures. The results indicated that the nanocomposites were synthesized effectively and Ag-Cu2O nanoparticles with the mean diameter of 27 nm were well dispersed on the LrGO. The conversion of methylene blue (MB) to Leuco Methylene Blue (LMB) and 4-Nitrophenol (4-NP) to 4-Aminophenol (4-AP) was performed by biosynthesized catalysts in the presence of NaBH4. The reaction rate of LrGO-Ag-Cu2O nanocomposite during 4-NP and MB reduction was found as 0.0026 s(-1) and 0.0497 s(-1), respectively. The LrGO-Ag-Cu2O nanocomposite showed superior catalytic performance for the reduction of both textile dyes.