The accurate measurement of low-frequency signal is the main research focus at present. Aiming at the problem that FBG accelerometer is difficult to measure vibration signal efficiently, we propose a low-frequency FBG accelerometer based on dual mass. Build the vibration model of the sensor, derive the theoretical formula of the sensitivity and resonant frequency, and use COMSOL software to optimize the design and simulation of the key parameters. According to the theoretical analysis results of finite element verification, the sensor is manufactured and its performance is tested. The experimental results show that the transverse crosstalk of the sensor is - 28.07 dB, the relative standard deviation of repeatability is 0.90%, the fitting determination coefficient R-2 is 99.98%, the sensitivity is 1194.91 pm/g, the dynamic range is 81.55 dB, the working frequency range is 1-40 Hz, and the inherent frequency is 58 Hz. In the low frequency band, the developed sensor exhibits good stability and sensitivity. This design provides a reference for the application of FBG accelerometer in low-frequency exploration.