An　interrogation　method　of　chirped　fiber　Bragg　grating　(FBG)　based　on　a　microwave　photonic　filter　(MPF)　is　proposed　to　realize　temperature-insensitive　strain　measurement.　In　the　proposed　MPF,　two　identical　chirped　FBGs　are　embedded　to　form　a　Michelson　interferometer.　When　strain　is　applied　to　one　of　the　chirped　FBGs,　its　wavelength　shift　will　produce　a　change　in　signal　transmission　latency　due　to　the　chromatic　dispersion　of　chirped　FBG,　resulting　in　a　path　difference　for　the　Michelson　interferometer.　Consequently,　a　variation　on　the　central　frequency　of　MPF　is　introduced.　Therefore,　the　wavelength　shift　of　chirped　FBG　induced　by　strain　can　be　interrogated　by　monitoring　the　frequency　response　of　MPF.　Moreover,　the　effect　of　ambient　temperature　can　be　compensated　with　the　other　chirped　FBG.　The　experimental　results　show　that　frequency　shift　of　MPF　in　response　to　strain　with　a　sensitivity　of　1.9　MHz/mu　epsilon　is　achieved　for　a　measurement　range　of　0　similar　to　1167　mu　epsilon.　Besides,　the　system　keeps　unchanged　within　a　temperature　range　from　30　degrees　C　to　100　degrees　C.