In this paper, based on Fabry–Perot cavity interference theory and spring diaphragm resonant system, a new optical fiber vibration sensing system is designed. Its vibration sensing principle is analyzed theoretically, and the finite element model is constructed by solidworks. The modal analysis and vibration characteristic response analysis of the sensor are carried out. The multi-peak demodulation algorithm is used to realize the real-time acquisition of the absolute cavity length, which has the advantages of high resolution and large dynamic range, and can adapt to the situation that the cavity length varies greatly. The dynamic response characteristics under the periodic frequency change are investigated through experiments, and the experimental results show that: the effective frequency range of the sensor is 5-200 Hz, the resonant frequency is 260 Hz, the low frequency band of 5-20 Hz has a flat amplitude-frequency response curve, the lowest detection acceleration is 0.1 m/s2, the sensor works stably under 0.1-10 m/s2 acceleration, the axial sensitivity is 8.19 μm/g, and the acceleration resolution is 1.5?10-5 g. It can be used to monitor the low frequency infrasonic wave of pipeline leakage.