The method of intensity demodulation with matched fiber Bragg gratings (FBG) is introduced. The FBG whose reflection spectrum overlaps with that of sensor FBG is selected to demodulate signals by detecting the changes of the intensity of reflected laser of demodulation FBG. The question that the intensity of reflected laser is a Gauss function of strain, i.e., two-values question caused by this method in strain sensors is studied. And a novel method that demodulation FBGs with well selected Bragg wavelength and bandwidth are in parallel connection is deduced so that the intensity of reflected laser is linear with strain. A theoretical model is set up and formulas are deduced. Finally this method is proved by experiment with two demodulation FBGs to be practicable and the sensor range is 522 με and the sensitivity is 2.6 με.