In this paper, the optical fiber Fabry-Perot (F-P) interferometer based on phase-shifting technique and birefringence crystals is proposed and demonstrated. We use the characteristics of birefringence and four birefringence crystals with different thicknesses to obtain the quadrature phase-shifted signals, which are demodulated by phase-shifting technique. Two types of sensing interferometers are used in the experiment. One is the optical fiber F-P sensor and the other is composed of the fiber end face and the glass surface fixed on the nanopositioning stage. The experimental results show that the normalized standard deviation (SD) of the calibration microphone centerline is 1.97 and 2.63 times larger than the optical fiber F-P interferometer under the sinusoidal sonic signals of 21 kHz and 40 kHz, and the interferometer is effective in avoiding phase ambiguity. The proposed interferometer has high stability and can adapt to a larger measurement range.