The driving and detection modal resonant frequency difference (Δf) of MEMS gyro structure is the main factor that determines its mechanical sensitivity. When Δf≈0, the gyro is in the frequency tuning state, and the mechanical sensitivity of the gyro reaches the maximum value. In this article, a capacitive fully symmetric S-shaped elastic beam silicon ring wave gyro is presented. In the process of frequency tuning with frequency modulation voltage, there is a certain stiffness coupling between the modes. This article analyzes that the reason for the stiffness coupling between modes is the structural error. The structural error of ring harmonic oscillator is mainly reflected in two vibration parameters. One is frequency, and the other is damping. Since the main parameter of frequency modulation voltage change is the stiffness coefficient, this article only conducts modeling analysis on the frequency error. Firstly, the structure of ring gyro is introduced, and the principle of electrostatic negative stiffness is analyzed based on this structure. Secondly, the causes of frequency error are analyzed, and the influence of frequency modulation voltage on the two operating modes is deduced by modeling. Finally, by comparing the theoretical model with the experimental results, the correctness of the theoretical derivation is evaluated, and the sensitivity of ring gyro is increased by 2. 7 times under the condition of frequency tuning.