In this study, a novel dumbbell-shape graphene nanoribbon (DS-GNR) was proposed for use in electronic devices, such as strain sensors. The electronic band structure of various dumbbell-shape (DS) structures and its change under the application of strain were analyzed by using first-principles calculations. All the first-principles calculations were performed using density functional theory (DFT) as implemented in the SIESTA package. The DS-GNR has two single GNR (S-GNR) components. The narrow and the wider S-GNRs form the sensing part and electrode part of the DS-GNR respectively, and connect to each other directly. Due to the intrinsic properties of graphene, two different widths of S-GNRs demonstrate two different electronic properties simutaneously. It has an unpredictable potential for improving the performance of electronic devices by applying only carbon atoms. Further, the complex fabrication procedures of devices can be minimized by using the proposed structure. The electronic band structure of DS-GNR decreases as the width of DS-GNR increases. The different combinations of the electrode part and sensing part of DS-GNR affect the band gap of DS-GNR. Furthermore, the electronic band structure of DS-GNR shows a significant change as a function of strain loaded on its structure. Thus, the DS-GNR structure is applicable to a highly sensitive strain sensor because the electronic properties of this structure can be controlled by the width of GNR and the strain-induced electronic band structure change.