The determination of a low frequency shaking signals is significant work in the areas of manufacturing machines, earthquake vibration, geological observation, and structural health monitoring in civil engineering. A cantilever beam model using aluminum equal strength with a mass block is presented that conformed in the low frequency excitation estimation by fiber Bragg grating (FBG) accelerometer. According to the experimentation testing, the FBG acceleration sensor, whose resonant frequency is closed to 143 Hz, that is appropriate for monitoring and evaluation for the low frequency shaking signals within the amplitude wavelength shift of 40-120 Hz. The sensitivity signal of FBG accelerometer is approximately from 6.74pm/g to 26.64pm/g, these linearity fitting are greater than 99%. The results of this research provide a mention for improving FBG accelerometer of the similar shape that provide more information to make better the sensitivity coefficient of FBG accelerometer.