The characteristics of transmission spectrum of Fabry-Perot(F-P) cavity composed of two fiber Bragg gratings(FBG) are analysed in this paper. As the influence factors, bandwidth of FBG, phase factor of reflection coefficient of FBG and length of cavity are included. The changes of its characteristics caused by temperature and strain are dicussed. Then the method of how to design this kind of F-P cavity with single mode at the Bragg wavelength of FBG is provided. The numerical simulation spectrum and experimental result are also given.