This study investigates the effect of edgepassivation on graphene nanoribbons. The geometry of graphene is simple and regular, and infinite, planar structure can easily be created either by hand or by taking a single layer from the crystal structure of graphene. To create a device-like structure, the infinite sheet must be cut into a suitable shape. Such a shape, at least for electronic applications, and it is called graphene nanoribbon (GNR). A pristine graphene monolayer can be cut into elongated strips to form 1D structure, referred to as graphene nanoribbons (GNRs) which can be either metallic or semiconducting depending on the type and width of edges. On the base of series of simulations it is found that elements from I st , III rd and IV th group are used as passivated elements with Armchair and Zigzag nanoribbons instead of Hydrogen. Best characteristics for zigzag nanoribbons are presented by elements from I st group. All experiments are made with Gold and Copper. For armchair nanoribbons, best characteristic are shown by elements from III rd group. The experiment is made with Indium. For nanoribbon with zigzag shaped edge is used DFT (Density Functional Theory) with LDA (Local Density Approximation). The chiral index of such nanoribbon is (3, 3). For the calculations of armchair nanoribbon is used Extended Hückel method. The chiral index of such nanoribbon is (3, 0). In both cases the k-point are set to 1 x 1 x 100 for na, nb and nc, respectively. For nanoribbons with zigzag shaped edges, DFT calculations show that edge-state bands at Fermi level (EF) rise to a very large Density of States (DOS) at EF, while Density of States of the armchair nanoribbons shows an energy gap around Fermi level. After Band Structure and Density of State, Bloch State is calculated and plot. Bloch States can be used to investigate the symmetry of certain bands and how this may be releated to the transport properties. Looking at the respective Bloch function, the wave function at G and Z are real and there is a distinct difference between valence and conduction band Bloch functions. These findings can be useful for the prospective GNR-based devices.