By analyzing the requirement of the closed-loop control for the vibratory gyroscope, the behaviour of the self-oscillation system with automatic gain control was analyzed with averaging method to achieve system stability and stable equilibrium. The theoretic analysis and experiment show that the reference voltage must be larger than a critical value; the larger the reference voltage is, the larger the signal-noise-ratio is; the system phase error will cause the resonance frequency drift and decrease the vibrating amplitude; different constants of the low pass filters result in different time to achieve the stable states. The experiment shows the frequency accuracy of the close-loop self oscillation system is about ±8ppm in 10 minutes and vibration amplitude is about 0.1% error in an hour.