A method of demodulation wavelength with the dynamic extrinsic Fabry-Pérot (F-P) cavity is proposed. The reflected light of fiber Bragg grating (FBG) is modulated by the F-P cavity which is constructed of a piezoelectric ceramics (PZT). By the theoretical analysis, the modulated intensity varies with the length of F-P cavity as cosine-like. When PZT has a vibration driven by a sine voltage, the cosine-like signal moves, and a linear relationship between the signal curve shift and FBG wavelength offset is numerically simulated, which can be applied to FBG wavelength of demodulation. Utilizing a temperature measurement system made up of the F-P cavity and a FBG, the liquid temperature measurement is carried out at different temperatures. Linear relationship between variation of the liquid temperature and the displacement of cosine-like signal is proved when the temperature changes from 35 ℃ to 80 ℃, and the linear fitting degree reaches to 99.5%.