Resonator fiber optic gyro (R-FOG) is a novel optical sensor whose resonant frequency is changed due to the Sagnac effect. The digital closed-loop operation can eliminate the thermal drift in analog circuits and it will make the R-FOG system more flexible. Taking the resonant frequency deviation as the research object, a simple analytical model for the closed-loop locking technique is presented based on one-order inertial loop operation. Frequency locking technique in the digital closed-loop operation system is then studied. The optimum loop gain is achieved under a certain integral time constant. Using above optimum parameters, the loop is locked quickly and stably. Furthermore, the analysis is verified by experiments.