A fiber grating (FBG) vibration sensor based on a flexible hinge suitable for low-frequency vibration measurement was proposed, which realized high-precision measurement of low-frequency signals within a certain range in response to the needs of low-frequency vibration detection. According to the ideal structure model of the sensor, combined with the torque balance equation and the Lagrangian equation, the calculation method of the sensitivity and natural frequency of the sensor was given, and the structure of the sensor was analyzed by finite element using ANSYS software, and the first-order resonance frequency was obtained as 92.457 Hz. Through the performance test, the sensor has good flatness in the frequency range of 0.5 to 55 Hz, and the natural frequency is 91 Hz, which is consistent with the finite element analysis result. The sensitivity is 1.94 nm/g and the linearity is 99.99%. The longitudinal sensitivity is much better than the lateral sensitivity, and it has strong lateral anti-interference ability.