In this study, the lubricity of perfect, and defective graphene on the gold substrate (Au (111)), has been investigated by using molecular dynamics simulations. The influence of surface morphology as well as the Stone-Wales (SW) defects concentration on the friction of graphene on the gold surface is explored. The SW defects in the range of 0–2.55% are randomly distributed into the graphene. Furthermore, the self-affine fractal method is employed to generate realistic rough surfaces. The effect of the external force, , in the range of , on the drag coefficients is investigated, too. It is shown that the friction force slightly depends on the sliding velocity for all systems. We show that by increasing the defect concentration, the lubricity of graphene nano-sheet slightly decreases. Moreover, it is shown that the friction almost insensitive to the roughness degree, within the range studied. Both of these effects can be rationalised through variations in the real atomic contact area.