The fiber Bragg grating sensor has a broad application prospect, and the main obstacle limiting its practical application is the high speed and high precision demodulation of the sensing signal. A matching grating filtering demodulation method and system were introduced. The reflectance matching filtering demodulation method was numerically simulated, and the strain transfer model was improved to establish a three-layer model of fiber-adhensive-piezoelectric stack. The specific parameters of fiber Bragg grating bonding on the piezoelectric stack were determined by simulation. Finally, the matching demodulation system was constructed. The method of expanding the demodulation range by bonding multiple fiber Bragg gratings on the piezoelectric stack was explored, and the center wavelength demodulation of fiber Bragg grating was realized by Hilbert transform peak-finding algorithm. The demodulation range of the system is 1 540.121 nm~1 541.474 nm, the maximum deviation is 8.6 pm, and the mean fluctuation is 5.4 pm, whose demodulation range, precision and stability are good, which can meet the wavelength demodulation requirements in specific applications. The demodulation system has certain reference significance and practical values.