To meet the requirements for low-frequency vibration monitoring, a new type of FBG (fiber Bragg grating) accelerometer based on diaphragm-type cantilever is proposed. The theory analysis of the structure was carried out and the finite element model was constructed to simulate and analyze the acceleration sensing characteristic of the sensor. Simultaneously, the tested results of sensing characteristic from the shaking table indicate that the system has excellent response to low-frequency acceleration excitation signal when the natural frequency of the system is 90 Hz. The frequency response range of the system is 5.0-60.0 Hz, in which the acceleration sensitivity is 485.75 pm/g. The acceleration sensor is designed with strong lateral immunity since the sensitivity in the transverse sensitivity is only 3.6% of the sensitivity in the working direction.