Aiming at the structure and stability problems of the single axis Interferometric Fiber Optic Gyroscopes (IFOG), fiber Lyot depolarizer was introduced in the light path system. Due to the new structure of the light path system, the very low polarization natural light was obtained in the gyroscope to ensure the accuracy and stability of the gyroscope. Using Jones matrix and coherence matrix, the model of interferometric fiber optic gyroscope system was established for the simulation analysis of the zero bias, and the result was verified by experiment. It was obvious that the light path system could maintain high accuracy and stability of the gyroscope system with the lower requirements of the polarization of the light.