A closed-loop resonant fiber optic gyroscope system using a fixed frequency narrow linewidth laser as the interference light source is proposed. The system uses a phase modulator to perform frequency shift control of the interference light to complete the tracking and locking of the resonant frequency in the counterclockwise direction of the resonant cavity. In this paper, a Simulink model of the gyro system was established and the output characteristics of the gyro were simulated at different speed points. The results show that the lock time of the counterclockwise resonance frequency in the range of ±200(°)/s is less than 15ms, and the gyro scale factor nonlinearity is 241ppm. Compared with the closed-loop resonant fiber optic gyroscope system using traditional frequency tunable narrow linewidth lasers, the frequency lock time and scale factor nonlinearity of the two systems are basically the same. This research provides theoretical and data support for the realization of low-cost closed-loop resonant fiber optic gyroscope system.