Based on the principle of intensity interrogation, the sensitivity of the fiber Bragg grating Fabry-Perot interferometer (FBG-FPI) strain sensor is analyzed and the influences of the grating length, the effective refractive index change and the cavity length of FBG-FPI resonator on the maximum strain sensitivity are also discussed. The strain sensitivities of two structures which FBG-FPI fibers are affixed to the transducer by different ways are also considered. The comparison between FBG-FPI and single fiber Bragg grating as well as traditional fiber Fabry-Perot interferometer with intensity interrogation is also presented. It is shown that the minimum theoretically detectable strain of the FBG-FPI strain sensors with intensity interrogation should be on the order of 10-12. The corresponding experiments, in which a periodic strain stimulated by a piezoelectric (PZT) affixed to the FBG-FPI, show that such a FBG-FPI strain sensor can be used to detect weak alternating strain signal and it has good linear character after the non-linear correction.