The intelligent structural health monitoring method, which uses a fiber Bragg grating (FBG) sensor, is a new approach in the field of civil engineering. However, it lacks a reliable FBG-based accelerometer for taking structural low frequency vibration measurements. In this letter, a flextensional FBG-based accelerometer is proposed and demonstrated. The experimental results indicate that the natural frequency of the developed accelerometer is 16.7 Hz, with a high sensitivity of 410.7 pm/g. In addition, it has a broad and flat response over low frequencies ranging from 1 to 10 Hz. The natural frequency and sensitivity of the accelerometer can be tuned by adding mass to tailor the sensor performance to specific applications. Experimental results are presented to demonstrate the good performance of the proposed FBG-based accelerometer. These results show that the proposed accelerometer is satisfactory for low frequency vibration measurements.