To meet the needs of three-dimensional vibration signal measurement in vibration measurement, a fiber Bragg grating three-dimensional acceleration sensor was designed based on flexible hinge. The vibration model of the pickup mechanism of the sensor was constructed, the structural model and measurement principle of the sensor were introduced, the theoretical formulas for the resonant frequency and sensitivity of the sensor were deduced, the mathematical model of the pickup mechanism was established, and the key dimension parameters of the pickup mechanism of the sensor were optimized and designed by MATLAB. The sensor was fabricated according to the optimized dimension, and its performance was tested by vibration experiments. The experimental results show that the resonant frequencies of the sensor in the X-axis, Y-axis and Z-axis directions are 673, 667 and 1376Hz, respectively, the operating frequency ranges are 0~220Hz, 0~220Hz and 0~450Hz, respectively, and the sensitivities are 72.3, 70.2 and 83.1pm/g, respectively. The designed sensor has good lateral anti-interference degree and can meet the requirements of three-dimensional vibration signal measurement.