A medium- and high-frequency fiber Bragg grating (FBG) accelerometer based on a circular flexure hinge structure is proposed. First, the sensor's operating theory and theoretical model are established. Second, MATLAB software was used to optimize the sensor construction, resonance frequency, and sensitivity, while ANSYS software was used to assess the viability of the optimization results and the modal analysis. Then, the actual product is manufactured, and the simulation results are used to calibrate the vibration sensor. The experimental results and theoretical values agree reasonably well. The FBG sensor's measured resonance frequency is approximately 1700 Hz, and its average sensitivity is 23 pm/G. The suggested sensor can measure vibration acceleration across a wide frequency range of 500–1400 Hz. Aircraft, missiles, earthquake research, intelligent compaction rollers, airbag deployment systems, and electronic stability control systems in automobiles are notable applications of this vibration sensor. These systems operate at medium and high frequencies.