The material structures in nature are so various. Some of the structures are regular and some else show interesting characteristics. There are Special types of structures that have interesting features due to existence irrational periodicity. These structures of regularities are called incommensurate systems. There are different models to investigate the effect of incommensurable potentials in different structures. Since the tight-binding model is a suitable model for study of the electronic properties of materials, therefore we consider it in our work. The Harper model is a form of tight-binding model that incorporates quasi-periodic potential. This model explains the sinusoidal potential network with a quasi-periodic frequency that influenced by the substrate potentials. The quasi-periodic potential can be produced in real systems as the mismatch of a two-dimensional (2D) layer with the underlying sublattice. Therefore we use the Harper potential for investigating the quasi-periodic potential on honeycomb lattice of Graphene and Nano-ribbons. In this thesis we investigate the localization transition in Graphene Nano-ribbons (GNRs) and two dimensional Graphene under the quasi-Periodic potential with Harper model. We compare Geometrical averaging of locale density of states with arithmetic averaging as a criterion for localization transition. We do it by exact diagonalization method using the LAPACK library functions. The results of this calculation method support also the results calculated in one-dimensional systems. The Inverse Participation Ratio (IPR) is another way to achieve the results. We reviewed it for one-dimensional systems in the states (considering the degenerate) at Fermi Energy. We find that it is completely consistent with the results the other methods. We also computed the IPR in the states of corresponding to the Fermi Energy in zGNRs and aGNRs to find the localization transition. The electronic properties of Nano-ribbons are strongly dependent on their width. So we consider a given Nanoribbon in the width specified under the Harper model and the same work was repeated for ribbons with different widths. These results show that there is a threshold for intensity of Harper potential in which all states around Fermi Energy are localized. In the zGNRs, which are metallic in the normal conditions, the threshold amplitude for the localization transition increase with increasing ribbon width, but it is exactly like to the one-dimensional systems in low widths. The same results obtained in narrow aGNRs which are metallic. However, the localization threshold for both of metallic ribbons increases with increasing width them. We also find that the application of quasi-periodic potential on semiconductor armchair ribbons leads to decrease of its gap. We have also calculated the Geometric mean (Gm) for local density of states and the Arithmetic mean (Am) for those in the Graphene, and the result was so interesting. Graphene as a purely two-dimensional material has a behavior similar to other materials when it is under the Harper potentials. Then it has localization phase like to metallic aGNRs and zGNRs and another materials such as one-dimensional systems in Harper model. For 2D Graphene, The localization threshold amplitude is more than these at metallic aGNRs, zGNRs and one-dimension systems. Keywords Graphene, Nano-ribbons, Harper model, Quasi-periodic, Inverse participation ratio, Local Density of State, Localization