Based on the Jones matrix of polarization-maintaining fiber, a model of Faraday nonreciprocal phase shift of a polarization-maintaining fiber coil is established. Calculation results show that the Faraday nonreciprocal phase shifts of the fiber coil have opposite polarity in the fiber＇s slow and fast axises, but are equal in size. A polarization alternately circulation polarization-maintaining interferometric fiber-optic gyroscope （PCPM-IFOG） is introduced that allows for the clockwise （CW） and counter clockwise （CCW） lights circle propagating around the coil once in the fiber＇s slow and fast axises separately. So the total Faraday nonreciprocal phase shift is zero and complete suppression on the effects of the Faraday nonreciprocal phase shift is achieved. Experiment results show the output of PCPM- IFOG with 500 m polarization-maintaining fiber coil, has no relation with the earth magnetic field. In contrast, the output Faraday bias drift of a polarization-maintaining interferometric fiber-optic gyroscope （PM-IFOG） with the same polarization-maintaining fiber coil is about ±0.3°/h when PM-IFOG azimuth angle is changed.