A polarization-insensitive fiber optic acoustic sensor is constructed with a 3x3 coupler and Faraday rotator mirrors. This system deals with the polarization-induced signal fading by a passive method. The method in eliminating polarization-induced signal fading and the output intensities of this system are described and demonstrated. The homodyne symmetric demodulation system used to recover the sensing signal is also analyzed in detail with experimental verification. The sensing head of this sensor is made of single mode optical fiber wound into a cylindrical shell with cast polyurethane rubber as the acoustic window. The sensitivity of this sensor is measured in anechoic water tank. The results show that this sensor has a stable receiving sensitivity of - 145.5 dB re 1V/?Pa and the bandwidth extends from 2 to 50 kHz. This sensor configuration can be used as a high sensitivity, wide band underwater acoustic sensor.