Graphene nanoribbons (GNRs), nano scale strips of graphene which consists of carbon hexagonal unit cell, are expected as next generation materials for high performance devices because of its unique super-conductive properties. When the strip width of graphene is cut into nano-scale, thinner than 70 nm, however, band gap starts to appear in the thin GNRs at room temperature, and thus, they show semiconductive properties. Previous studies have shown that the bad gap of GNR is highly sensitive to strain, which indicates that GNRs are candidates for a detective element of highly sensitive strain sensors. In practical applications, ohmic contact between a metallic electrode and a semiconductive detective element is indispensable for these sensors. By considering the effect of the width of GNRs on their electronic properties, dumbbell-shape GNRs (DS-GNRs) structures have been proposed for the basic structure of the GNR-base strain sensors, which consisted of GNRs with two different widths. Center portion of the DS-GNR is narrower than 70 nm and GNRs wider than 70 nm are attached at the both ends of the center GNR as electrode. Both semiconductive and metallic portions of a strain sensor consist of only carbon atoms using this DS-GNR structure. Even though this structure consists of one material, the effect of the interaction between two metallic and semiconductive GNRs must be clarified to realize the strain sensor with high performance. In this study, first principle calculations were applied to the analysis of the electronic band structure of the DS-GNR based on density functional theory (DFT). It was found that the local distribution of energy states of electrons and charges varied drastically as strong functions of the length of GNRs and the magnitude of the applied strain. The current through the DS-GNR structure was converged as the length of the semiconductive portion increased. In the models with enough length, transport property of the DS-GNR showed high sensitivity to strain. Thus, the effective resistivity of the structure varied from metallic to semiconductive, and therefore, this structure is appropriate for the next-generation highly sensitive and deformable strain sensors.