Significant interest has been focused on graphene materials for their unique properties as Hydrogen storage materials. The development of their abilities by modifying their configuration with doped or decorated transition metals was also of great interest. In this work, using the DFT/B3LYP/6-31G/LanL2DZ level of theory, graphene sheet (GS) as one of the materials of interest was doped with two transition metals, Osmium (Os) and Tungsten (W). Two active sites on the GS were tested (C4 and C16) resulted into adsorbed systems, H2@C4-GS and H2@C16-GS. C16 position showed the largest adsorption energy compared to that at C4. Therefore, C4 was replaced by the two metals and two adsorbed systems were formed: H2@Os-GS and H2@W-GS. The binding energy of H2@Os-GS was found to be greater than that of H2@W-GS.