A fiber grating acceleration sensor based on flexure hinge structure was designed. The structure theory analysis was carried out and the finite element model was built to simulate and analyze the acceleration sensing characteristic of the sensor. A fiber Bragg grating(FBG) acceleration detection system with temperature self-compensation was designed based on F-P filter, which achieved zero temperature self-compensation by adding a feedback circuit to control F-P filter. The characteristics of the system were tested on the built system. The results indicate that the system has excellent response to impulse excitation signal and continuous acceleration excitation signal. Natural frequency of the system is 380.0 Hz, while the dynamic range reaching 65.6 dB. The frequency response range of the system is 10.0 -240.0 Hz, in which the acceleration sensitivity is 236 pm/g. Since the sensitivity in the interference direction is only 3.5% of the sensitivity in the working direction, the acceleration sensor is designed with strong lateral immunity.