Pt nano-particles are supported on carbon materials at the electrode catalysts of protonexchange menbrane fuel cells. Pt nano-particles are desirable to be strongly adsorbed on carbon materials for high dispersion, although strong Pt-C interactions may affect the catalytic activity of small clusters. Thus we have examined H-atom absorption on Pt clusters supported or unsupported on graphene sheets, using first-principles calculations. For Pt-atom/graphene systems, a H atom is more weakly adsorbed than for a free Pt atom, and the H-Pt interaction becomes weaker if the interaction between a Pt atom and graphene becomes stronger. For the Ptn-cluster/graphene systems (n=2-4), the H-Pt interactions are also substantially changed from those for free Pt clusters. In the Pt clusters on graphene, the Pt-Pt distances are substantially changed associated with the electronicstructure changes by the Pt-C interactions. These structural and electronic changes in the Pt clusters as well as the presence of graphene itself seem to cause the changes in the absorption energies and preferential sites of H-atom absorption.