The adhesion of a graphene monolayer onto terminated or 2x1-reconstructed diamond (111) surfaces has in the present study been theoretically investigated by using a Density Functional Theory (DFT) method. H, F, O, and OH species were used for the surface termination. The generalized gradient spin density approximation (GG(S)A) with the semiempirical dispersion corrections were used in the study of the Van der Waals interactions. There is a weaker interfacial bond (only of type Wan-der-Waals interaction) at a distance around 3 Å (from 2.68 to 3.36 Å ) for the interfacial graphene//diamond systems in the present study. The strongest binding of graphene was obtained for the H-terminated surface, with an adhesion energy of -10.6 eV. In contrast, the weakest binding of graphene was obtained for F-termination (with an adhesion energy of -2.9 eV). For all situations in the present study, the graphene layer was found to retain its aromatic character. In spite of this, a certain degree of electron transfer was observed to take place from graphene to Oontop-, Obridge-, and OH-terminated diamond surface. In addition, graphene attached to Oontop-terminated surface showed a finite band gap.