An approach of fiber grating strain demodulation based on the principle of polarized-light interference is introduced, which can solve the so called cross sensitivity in the fiber Bragg grating sensor. To the yttrium vanadate (YVO4) crystal polarized-light interferometer, by choosing two different fiber Bragg gratings with a π rad phase difference, one as a strain sensor and the other for temperature compensating. The cross sensitivity can be conquered. The analysis of the strain demodulation resolution shows that with the decreasing of the crystal thickness the resolution increases. The experiment shows that when the thickness of the YVO4 crystal is 0.5mm the effect of cross sensitivity is reduced to 0.13 με/℃ which is 1.6% of the effect with only one fiber Bragg grating for strain measure and that when the thickness is 0.1 mm the cross sensitivity is reduced to 0.0067 με/℃ which is less than 0.08%. Reduced thickness of crystal benefits the resolution of strain measure but the machining of the small thickness crystal is difficult, and to solve this problem a new scheme of polarized-light interferometer with the structure of double layers crystal is analysed in the end.