The atomic-scale wear, the formation process of the graphene during the lateral line scan process of the nanoscale tip on the multi-layered graphene substrate is studied by using molecular relaxation method. The nanotip is scanned in line forward (along [1 2 -3 0] direction) and backward under the constant-height mode. Analysis of the effect of the tip height on the relative motion of the nanotip, the 1st graphene layer, and the 2nd graphene layer, reveals the transition from the nanotip state to the graphene tip state. During the nanotip state the mean lateral force <F_x> rapidly increases as the mean loading force <F_z> increases. Here the friction between the tip and the surface occurs. However, during the graphene tip state, <F_x> takes nearly the constant value independent of <F_z>. Here the internal friction among the 1st, the 2nd and the 3rd graphene layers occurs. The marked scan directional dependence and the increase of <F_x> near the graphene edge appears. The irreversible shift of the graphene layer after all the scan processes can explain the mechanism of the elementary process of the atomic-scale wear. [DOI: 10.1380/ejssnt.2009.173]