In order to realize the vibration monitoring in two directions of the surface, a fiber Bragg grating bi-directional accelerometer is designed based on the circular flexure hinge. First, the theoretical formulas of its resonant frequency and sensitivity are derived. Then, based on the theoretical formulas of circular hinge stiffness, the empirical formulas of hinge stiffness are derived and verified. The mathematical model of the sensor is optimized by MATLAB, and the size parameters are obtained when the sensitivity of the sensor reaches the maximum as the work needs are satisfied. The experimental results show that the resonant frequency is about 368 Hz, the sensitivity is about 107.3 pm/g, and the transverse anti-interference degree is around 4.8%. The error between the theoretical value and the actual value of the resonant frequency and sensitivity are -4.2% and 7.0% respectively.