Slow light technology has been greatly developed in the last decade. Many mechanisms have been used to slow down the velocity of light, and its potential applications have been continuously researched. In this paper a novel high spectral sensitivity optical fiber interferometer with slow-light medium is proposed, and it is applied to enhance the wavelength detection sensitivity of fiber brag grating (FBG), accordingly the sensitivity of FBG would be enhanced greatly. Finally, position sensitive detector (PSD) is used to demodulate the interference fringes of the optical fiber interferometer.