As is well known, the surface topography strongly determines the tribological performance and all practical surfaces are rough. Since the actual friction process has apparently random characteristics, in order to obtain the friction suitable to the rough surface, it is necessary to set up a random friction model. In the present paper, the friction between a randomly roughness surface and an atomic-level smooth rigid plane is studied based on the Lennard-Jones potential model. A micro friction model is proposed. In the model, the potential energy between interfaces is determined by the normal load and the balanced spacing. With the numerical technique, the frictional force is calculated and the relationship between the frictional force and the normal load is analyzed as well. The results show that the friction force increases with the normal load increasing, but it increases nonlinearly. The results also show that the interfacial potential may be an essential origin of micro friction.