In this research, at the first project, graphite nanosheets were covalently functionalized through oxidation and sulfonation. The functionalized graphene layers were characterized by several techniques and their thermal properties were investigated. Then biodegradable polycaprolactone (PCL) was grafted on graphene surface. The fabricated composites were investigated and studied by different analytical methods such as FT-IR, CHN, XRD, TGA, DSC and FE-SEM. Also TGA data showed that the thermal stability of composite was increased after grafting of functionalized graphene. The nanocomposites with different percentage PCL-grafted-functionalized graphene were prepared and the mechanical properties of the nanocomposites were studied. The elastic modulus, tensile strength, and strain were also obtained. The results showed that by increasing the slight percentage of functionalized graphene in polymer tissue, mechanical properties of the nanocomposites were improved. At the next project, polystyrene (PS) was grafted on sulfonated graphene (SG) edge. The fabricated composite was investigated and studied by different analytical methods like FT-IR, CHN, XRD, TGA, DSC and FE-SEM. The nanocomposites with different percentages PS-grafted-SG were prepared by casting method. The mechanical properties of the nanocomposites were also studied. The thermal stability, elastic modulus, tensile strength, and strain were obtained from this investigation. The results showed that by increasing the percentage of functionalized graphene in polymer tissue, mechanical properties of the nanocomposites did not change much. Morphological studies of prepared composites proved grafting of PCL and PS on functionalized graphene surface.