Micro-hemispherical resonator gyroscopes are widely used in aerospace, precision navigation and other fields due to their high stability and accuracy. However, the orthogonal error caused by structural defects seriously limits the application of microhemispherical resonator gyroscopes in high-precision scenarios. Firstly, the mechanism of orthogonal error is analyzed by a dynamic model considering the damping-mass-stiffness coupling effect. Then, based on the analysis of the orthogonal error mechanism, a micro-hemispherical resonator gyroscope orthogonal error compensation system based on the orthogonal coupling stiffness correction method is designed. Electrostatic negative stiffness is generated through a dedicated orthogonal control electrode configuration to directly offset the orthogonal coupling stiffness. Finally, a closed-loop compensation system is implemented and test verification is carried out. The test results show that after compensation by orthogonal coupling stiffness correction method, the angle random wander of the micro-hemispherical resonator gyroscope is reduced from 9.767°/$h$ to 1.327°/$h$, the zero bias instability is reduced from 2.884°/h to 0.047°/h, and the zero bias stability is reduced from 29.954°/h to 0.402°/h after 10 s smoothing. The performance of the gyroscope has been significantly improved after compensation, which verifies the effectiveness of the orthogonal coupling stiffness correction method. The research strongly promotes the development of inertial navigation systems.