In this paper, we propose a novel method of the demodulation of FBG sensing system based on chirp grating and LPG edge filter in which chirp grating is used as band filter. The measurement speed is mainly determined by the response time of the photo-detector and the convert time of AD chips. So, it can highly improve the stability and scan speed of the sensing system. In the experiment system, we use fiber Bragg grating and adjust its bandwidth to get a chirp grating.. The center wavelength of chirp grating is 1551.60nm, and the pass-band wavelength is 7nm. The LPG is written on a standard single mode fiber with microlens array. The grating has a period of 440μm and a length of 3 cm. The center wavelength of LPG is 1558nm, and the falling edge of LPG is from 1540nm to 1555nm. We investigate light power by using a monitor magnify circuit, while the reflected wavelength of FBG by using optical spectrum analyzer. This system has high linear output and the linear fitting is 0.9918. The windage is due to the non-perfect square spectral profile of the reference chirp fiber grating.