A double-arched-beam-based fiber Bragg grating (FBG) sensor for displacement measurement is presented. Unlike most FBG sensors that measure the resonance wavelength shifts to detect the measurand, this kind of FBG sensor is proposed to measure the displacement based on the demodulation of the FBG's reflective spectra bandwidth. According to the strain distribution on the novel double-arched beam surface, the positive and negative strain will act on only one FBG, which is stuck on the beam surface. Thus, the positive and negative strain will make the spectra broaden as the displacement increases. What is more, the problem of cross-sensitivity in the FBG sensor is solved because temperature only affects the wavelength shift, but not the spectra bandwidth. Simulation and preliminary experimental results indicate the feasibility of the proposed idea and a fairly good linearity of the measurement characteristic.