Graphene shows unique super-conductive properties and graphene nanoribbons (GNRs) with band gaps are the candidates for a sensing component of highly sensitive strain sensors. Usually, there is a large energy barrier between electrodes and semiconductors which is not suitable for electron transfer. Therefore, ohmic contact between them is indispensable for fabricating electronic applications. In order to achieve the ohmic contact between external electrodes and detective elements in the devices, the dumbbell-shaped structure of GNRs was proposed for the basic structure of the GNR-based strain sensors, dubbed as dumbbell-shape GNR (DS-GNR). It consists of a long narrow GNR at the center of the structure as the sensing element coalesced with two wider GNRs at both ends of the narrow GNR as the contact components to external electrodes. Both narrow and wide segments of DS-GNR consist of only carbon atoms. The effect of the interaction in the vicinity of the junction area between wide metallic and narrow semiconductive GNRs, however, has not been clearly demonstrated. In this study, first-principles calculations were implemented to the analysis of the electronic band structure of the DS-GNR. It was found that the localized distribution of the energy states of electrons exists in the wide segment of DS-GNR. The changes varied from wide to narrow segment is smooth and observable as strong functions of the length and the width of DS-GNRs. The current-voltage characteristics showed curved semiconductive-like electronic properties with a smooth-electron flow in DS-GNR. Therefore, the DS-GNR has great potential for the use of next-generation highly sensitive and deformable strain sensors.