We examined atomic and electronic structures of Pt supported on graphene, using the first-principles calculations based on the density functional theory (DFT). First, we examined the interaction between graphene and a Pt(111) monolayer. The stable distance between graphene and the Pt-monolayer is 3.48Å and the adhesive energy is 0.09 eV/atom. The density of states (DOS) for the Pt(111)/graphene system is the same with the sum of respective DOS's of the graphene sheet and the Pt monolayer. These results indicate that the interaction between graphene and a Pt(111) monolayer is very weak. Second, we examined the interaction between graphene and a Pt atom. The Pt-C bond length is 2.31Å and the adsorption energy is 2.82 eV/adatom, which means the stronger interaction. Finally, we examined the interaction between graphene and a Pt cluster consisting of ten atoms. The distance between graphene and the bottom layer of the cluster is about 2.7Å, which is shorter than that between graphene and the Pt(111) monolayer. This shows that the interaction between the Pt10 cluster and graphene is stronger than the Pt-monolayer/graphene interaction. The center atom in the hexagonal bottom layer of the Pt cluster has the nearest distance with graphene of about 2.5Å. If there is a defect on graphene, the center atom of the hexagonal bottom layer strongly interacts with that.