The transmission characteristics of a Fabry-Perot （F-P） interferometer based on a fiber Bragg grating （FBG） pair with a built-in long-period fiber grating （LPFG） are theoretically analyzed, and the shift of transmission interference fringe as a function of environmental refractive index is acquired. The influence of the lengths of F-P cavity, LPFG and FBG on the transmission characteristics of the proposed interferometer has been numerieaUy investigated, and the simulation results indicate that the sensitivity of refractive index reaches 2.27 × 10-6 for an optical spectrum analyzer （OSA） with a resolution of 1 pm.
