A flexible hinge fiber Bragg grating (FBG) acceleration sensor based on the symmetry mass block is proposed to address poor transverse performance and lower sensitivity in medium- and high-frequency. The dual mass block design causes the FBG fiber to vibrate while simultaneously being stretched or compressed in the reverse direction. Thus, the FBG's sensitivity is greatly improved, and its deformation is double that of the single hinge construction. MATLAB software theoretically investigates and optimizes the sensor's natural frequency and sensitivity. In contrast, ANSYS analyzes static structural stress and simulation. The implementation of the sensors is assessed through an experimental test. The accelerometer's natural frequency is 1550 Hz, and its working stability frequency range is flat at 400–1000 Hz. The amplitude anti-interference of the sensor is approximately 3.27%, and the average sensitivity's linearity is roughly 66 pm/g. Developing medium and high-frequency vibration data is essential for the health monitoring and evaluation of constructions such as bridges, railroads, and tunnels.