Tunable Fabry-Perot (F-P) filter-based demodulation methods are more used in the wavelength demodulation of fiber Bragg grating (FBG). However, the hysteresis and creep of the piezoelectric ceramic (Pb(Zr1-xTix)O3，PZT) in the F-P filter make the output wavelength of the F-P filter nonlinearly change with time, resulting in the problems of large wavelength demodulation error and low sensing accuracy. In this paper, we start with the study of hysteresis and creep characteristics of PZT in F-P filters, and propose an F-P filter-based wavelength demodulation method based on thermal etalon and hysteresis and creep compensation control of the PZT. The driving voltage of PZT is controlled to change nonlinearly with time so that the wavelength of the broadband light source output through the F-P filter can be changed at equal intervals with time.The peak wavelength of the etalon transmission spectrum is thus obtained and also changes linearly with time. It acts as a "tick" for the wavelength scale and provides an accurate wavelength reference for demodulating the wavelength of the sensing grating. The experimental results of the FBG temperature measurement show that, compared with the method without hysteresis and creep compensation control, the proposed method improves the temperature measurement accuracy about 20 times and the temperature measurement error is less than 0.5 ℃.