First-principles calculations have been applied to investigate the interactions between Ptn (n=1˜13) clusters and a graphene sheet to model the Pt/C fuel-cell catalytic electrode. For the small clustesr (n<7), planar configurations vertically adsorbed on graphene (V-2D) are more stable than the three-dimensional (3D) configurations. For the large clusters (n>7), the 3D clusters are more stable than the V-2D clusters. In order to investigate the effects of defects and dopants in a graphene sheet, the interactions between the Pt13 cluster and the graphene sheet with an atomic vacancy and an dopant atom, such as boron and nitrogen atoms have been examined. For the atomic vacancy, the Pt atom is directly adsorbed on the C atom vacant site. For the Pt13 cluster adsorbed on the graphene sheet doped with the B or N atoms, the Pt atom is not directly adsorbed on the impurity atoms. The adsorption of the Pt13 cluster above the vacancy of the graphene sheet is more stable that that on the doped graphene sheet in the present calculations.