Acceleration monitoring is an important technical means of seismic monitoring, oil exploration, deep well observation, etc. A miniaturized fiber Bragg grating (FBG) acceleration sensor with three cantilever beams is proposed against the fact that it is difficult for fiber-optic sensors to meet the requirements for low-frequency vibration monitoring. First, the model of the FBG acceleration sensor was built and theoretically analyzed; second, the effect of structural parameters on sensor sensitivity and natural frequency was analyzed, and the sensors were subjected to static stress analysis and modal simulation analysis through the ANSYS finite element analysis software; finally, the real sensors were developed and subjected to performance tests with a low-frequency vibration test system. According to the result, the natural frequency of the sensor is about 64 Hz, and its sensitivity is 201.3 pm/g; favorable linearity is observed at the working frequency band of 0.1-40 Hz, and the transverse interference is less than 2.51%. The research findings offer a reference for the development of like sensors and the further exploration of the lower limit of low frequency.