This article establishes a circuit model with which to analyze the difficulty of auto-gain control driving for low-Q micromechanical gyroscopes at room temperature and normal pressure. It also proposes a driving circuit based on frequency modulation to eliminate the same-frequency coupling between the drive signal and displacement signal using a second harmonic demodulation circuit. The results of the simulation indicate that a closed-loop driving circuit system based on the frequency modulation principle can be established within 200 ms with a stable average frequency of 4504 Hz and a frequency deviation of 1 Hz. After the system was stabilized, the root mean square of the simulation data was taken, and the frequency jitter was 0.0221 Hz.