In this study, a high-resolution optical fiber Fabry–Pérot (FP) interferometer displacement sensor with chirped spectral characteristics based on a tapered microfiber is theoretically discussed and experimentally implemented. Instead of inscribing two fiber Bragg gratings (FBGs) on the symmetric position of the microfiber, we continuously inscribed one long FBG along the microfiber region to reduce the cavity length. The bandwidth of the interferometer is over 35 nm, and its displacement sensitivity is as high as 36.5 nm/mm at the tension state.