The effect of the periodically aligned edge defects in graphene nano-ribbons (GNRs) on their electronic properties was analyzed by using density functional theory. The typical two structures of GNRs such as zigzag (ZGNR) and armchair (AGNR) structures were employed for the analyses. It was found that the electronic structures of GNRs changed significantly by their deformation caused by the applied mechanical stress. The electronic band structure of the armchair-type GNRs changed periodically as a function of the number of carbon atoms along their width direction. In addition, the peak amplitude of the band gap decreased monotonically with their width. The peak position also changed clearly by the introduction of the edge defects. Therefore, the electronic properties of GNRs vary drastically depending on their quality, in other words, the order of atom arrangement.