A metal bellows-based fiber Bragg grating (FBG) accelerometer is proposed and experimentally demonstrated. The optical fiber (containing the FBG) is pre-tensioned, and the two ends of the optical fiber are fixed directly from the shell to the inertial mass. In this design, the FBG is uniformly tensioned to obtain a constant strain distribution over it. By employing this configuration, the FBG always has a sharp reflection characteristic with no broadening in its reflection spectrum during wavelength shifting. Dynamic vibration measurements show that the proposed FBG accelerometer has a wide frequency response range (5–110 Hz) and an extremely high sensitivity (548.7 pm/g). The two important indicators of FBG accelerometer can be tuned by the addition of mass to tailor the sensor performance to specific applications, identifying it as a good candidate for structural health monitoring.