Molecular dynamics simulation and the two-temperature method are carried out to model the effects of substrate roughness as well as electron–phonon coupling on thickness-dependent friction on graphene. It is found that substrate roughness can significantly enhance friction of graphene, which is orders of magnitude larger than that on smooth substrate due to puckering effect. Additionally, the adhesive force between graphene and substrate plays opposite roles for smooth and rough substrates. While on a smooth substrate, a larger adhesion hinders the wrinkle formation in graphene, therefore suppressing friction, on a rough substrate, adhesion helps induce atomic roughness in graphene and leads to friction enhancement. We also incorporate electron–phonon coupling into the atomistic modelling through a two-temperature method, and discover that its effect on friction is very small compared to that of roughness.