A novel method of a fiber Bragg grating (FBG) stain sensor demodulation technique is presented. An experimental system is built up in which high birefringence fiber (HBF) Sagnac loop mirror (LM) is used as the edge filter. In order to improve the temperature stability of the system, we have experimentally demonstrated that packaged HBF can compensate the temperature shit of the HBF Sagnac LM filter. The shift of wavelength for an uncompensated HBF Sagnac LM is approximately 2.3nm/0C, and that of the compensated HBF Sagnac LM is 0.03nm/0C, which is much less than that of the uncompensated HBF Sagnac LM filters. Using the temperature-compensation HBF Sagnac LM, We achieve linear demodulation of FBG strain sensor with a range of about 1900 and the strain sensitivity is about 0.14 w/ .