High-precision and high-sensitivity vibration acceleration sensors have been a research hotspot in engineering technology, which play an important role in engineering structural health monitoring, earthquakes, tsunamis, and geological exploration. A novel, to the best of our knowledge, fiber Bragg grating (FBG) acceleration sensor incorporating a mass block and flexible hinge was proposed against the low sensitivity and poor transverse interference resistance of existing FBG acceleration sensors. The FBG accelerometer with the multi-stage flexible hinge was modeled and theoretically analyzed, the structural parameters of the sensor were optimized and actual sensors were developed, and a sensor performance test experiment was carried out in the end. The result suggested that the sensor's natural frequency was as high as 1400 Hz, and its response was flat in the frequency range of 50-800 Hz; its sensitivity was 18.4 pm/g, linearity R 2 was 0.9983, and transverse interference immunity was below 3.2%. The research findings offered a new way of thinking about high-precision and high-sensitivity vibration measurement in engineering technology.