In this research, we study the electronic properties of two pure graphene ribbon and their adducts by adding the Al / N compound. We showed that the electronic softness of the pure Graphene Ribbon was increased with increasing the thickness of the Ribbon, adding the Al / N atoms leads to decrease the electronic softness. The electrochemical hardness has inversely behavior to the softness. Increasing the thickness of the Graphene Ribbon leads to decrease the forbidden energy gap of the Ribbon, but the energy gap is increase due to the addition of the Al / N atoms in the Ribbon