A fiber optic accelerometer with a high sensitivity, low noise, and compact size is proposed for low-frequency acceleration sensing. The sensor is composed of a 20 mm diameter spherical outer frame and a three-dimensional spring-mass structure as the inertial sensing element. Three Fabry-Pérot interferometers (FPI) are formed between flat fiber facets and cubic mass surfaces to measure the FPI cavity length change caused by acceleration. The dynamic signal sensing of the designed accelerometer is performed, which shows a high acceleration sensitivity of 42.6 dB re rad/g with a working band of 1-80 Hz. An average minimum detectable acceleration of 4.5 µg/Hz1/2 can be obtained. The sensor features simple assembling, small size, light weight, and good consistency. Its transverse sensitivity is measured to be less than 3% (-30 dB) of the sensitive axis. The experimental result indicates that the proposed accelerometer has application potential in areas such as seismic wave detection and structural health monitoring.