A microwave photonic filter based on photonic crystal fiber Lyot-Sagnac loop was presented,the filter′s center frequency can be continuously tunable. The length of the photonic crystal fiber is 11.94 m and 1.94 m,using the thermo-sensitive liquid of Cat.19340 to fill one big hole of the two photonic crystal fibers and then embed them into Lyot-Sagnac loop. Simulation analysis of the effect of different duty ratios to the period of comb spectra of Lyot-Sagnac loop and the tuning range of the passband center frequency of the filter. The result shows that the larger the duty ratio,the smaller the period of comb spectra of Lyot-Sagnac loop and the larger tuning range of the passband center frequency of the filter. In the case of the maximum duty ratio,when the effective length of the two photonic crystal fibers is 10 m,the simulation measured period of comb spectra of Lyot-Sagnac loop at the temperature of 20℃ and 80℃ is 0.36 nm and 0.26 nm,when the effective length is 13.88 m,the measured period of comb spectra is 0.26 nm and 0.19 nm respectively. Using the Lyot-Sagnac loop to slice the broadband light source,by adjusting the thermo-sensitive liquid′s temperature from 20℃ to 80℃ and the polarization controllers inside the ring,the wavelength of the light source can be tuned within the range of 0.19 nm~0.36 nm,the center frequency of the microwave photonic filter can be tuned continuously within the range of 31.04 GHz~58.81 GHz.