Abstract: According to the ideal approximation of the coupled-mode theory, the Bragg equation and the peak reflectivity expression of the fiber Bragg grating are derived. The relationship between the grating spacing, the grating length, the max of refractive index micro-disturbance and the reflectivity is analyzed. The simulation result shows the least narrow bandwidth of Bragg grating under the defined parameters is 0.02nm when its reflectivity is 1, which is much narrower than the fiber Bragg grating used in typical distributed sensor system. It is proved that this fiber Bragg grating can be used as a fiber grating sensor for distributed demodulation system, which will improve the bandwidth availability of light source in the distributed sensing systems, increase the number of sensing Bragg gratings, eliminate the crosseffect between signals, and reduce the cost of the demodulation system.