For the random fluctuation of nonlinearity curve of fiber Fabry-Perot tunable filter (FFP-TF) increasing in temperature changing environment, which results in the instability of fiber Bragg grating (FBG) demodulation system, a novel method based on auxiliary optical fiber Michelson interferometer (AFMI) to stabilize demodulation performance is proposed. The optical frequency subdivision in wavelength interval of Fabry-Perot etalon is achieved, and the demodulation algorithm by local optical frequency subdivision is compiled. Under temperature changing environment, we investigate amplitude of fluctuation by an AFMI, whose spectral interval is 9.53 GHz. The experiment shows that the amplitude of fluctuation is ±28.5 pm without AFMI, and standard deviation is 8.6 pm. However, the amplitude of fluctuation is ±3.5 pm with AFMI, and standard deviation is 1.4 pm. The wavelength demodulation stability of fiber Bragg grating in temperature-variable situation is effectively improved.