In recent years, the application prospects of high-precision MEMS gyros have been shown to be very broad. Honeycomb disk resonator gyroscope (HDRG) has many advantages including higher immunity to interference, better vibration symmetry and better electrodes arrangement, which shows excellent potentials in MEMS gyros. The material of HDRG is silicon. The frequency drift cannot be avoided under variable temperature environment and becomes one of the important factors causing the bias drift of MEMS gyros, while there is little research on that. This paper analyzes the characteristics of frequency drift and proposes a resonant constant-frequency (RCF) control method to suppress the bias drift in HDRG. Different from the previous work, this paper proposes a new RCF control method by controlling the excitation frequency of the gyro, and the effect of frequency drift on the zero-rate-bias (ZRB) of HDRG is quantitatively investigated, which the variation of 1Hz in working frequency can cause a $12.30^{\circ}/\mathrm{h}$ ZRB change. Finally, experiments have verified the effectiveness this method.