The geometry, electronic properties and energy of the complexes formed between an extended graphene and polycyclic aromatic hydrocarbons,PAHs, were investigated at the Density Functional Theory (DFT) level. We have studied the interaction of benzo[a]pyrene, chrysene, benzo[a]anthracene and benzo[b] fluoranthene with graphene models of dimensions of 15 Å, × 15 Å and 20 Å × 20 Å. These calculations were performed within the generalized gradient approximation GGA using the HCTH functional and the numerical DNP basis set. According to the results, the HCTH/DNP methodology can qualitatively describe attractive interactions occurring between the weakly-polar systems, verifying the formation of molecular complexes stabilized by Keesom or Debye forces. The interaction dipole moments and polarizabilities indicate that the interaction of permanent dipoles and induced dipoles are responsible for the complex formation in weakly polar PAHs. These results are useful to understand the processes of adsorption of PAHs by graphene.