We proposed a scheme of fiber Bragg grating (FBG) sensor interrogation system based on all fiber Mach-Zehnder Interferometer (MZI) edge filter and tunable-FBG. The equal power signals from FBG sensor and tunable FBG are coupled into port 1 and port 2 of MZI respectively. The experimental results show that the interrogation precision of the proposed system is 0.02 nm in a range of Inm. Furthermore, the precision can be improved by adjusting the two interference arms of the filter.