Ab initio vdW calculations with the DFT level of theory were used to investigate hydrogen (H₂) adsorption on Pt-adsorbed graphene (Pt-graphene). We have explored the most energetically favorable sites for single Pt atom adsorption on the graphene surface. The interaction of H₂ with the energetically favorable Pt-graphene system was then investigated. We found that H₂ physisorbs on pristine graphene with a binding energy of -0.05 eV, while the binding energy is enhanced to -1.98 eV when H₂ binds Pt-adsorbed graphene. We also found that up to four H₂ molecules can be adsorbed on the Pt-graphene system with a -0.74 eV/H₂ binding energy. The effect of graphene layer stretching on the Pt-graphene capacity/ability for hydrogen adsorption was evaluated. Our results show that the number of H₂ molecules adsorbed on the Pt-graphene surface rises to six molecules with a binding energy of approximately -0.29 eV/H₂. Our first-principles results reveal that the Young's modulus was slightly decreased for Pt adsorption on the graphene layer. The first-principles calculated Young's modulus for the H₂-adsorbed Pt-graphene system demonstrates that hydrogen adsorption can dramatically increase the Young's modulus of such systems. As a result, hydrogen adsorption on the Pt-graphene system might enhance the substrate strength.