The electronic properties of graphene nanoribbons (GNRs) have a function of the ribbon width. It can vary from metallic-like ones to semiconductive-like ones when the width of single GNR is changed. Therefore, the novel structure of GNRs called dumbbell-shape GNR (DS-GNR) was proposed to achieve the development of highly sensitive, reliable, and deformable strain sensors. The DS-GNR consists of one long narrow GNR coalesced by two wide segments of GNRs at its both ends. The wide segments of the original DSGNR possess the metallic-like electronic properties and the narrow segment of the original DS-GNR has the semiconductive-like electronic properties. In this study, the strain-induced change of the electronic band structure of DSGNR was analyzed by using the first-principles calculations. The range of the applied uniaxial tensile strain on DS-GNR was from 0% to 10%. When the length of the narrow segment of DSGNR is longer than 4.3 nm, the effective bandgap located in the narrow segment changes obviously with the change of applied strain. The result indicates that the piezoresistive effect appears in the narrow segment of DS-GNR, and thus high strain sensitivity of its resistivity can be applied to strain sensors.