Aiming at the structural vibration problems in a wind turbine caused by the dynamic stiffness of the drive-train system, a quantitative analysis model with time-varying gear mesh stiffness is established that takes into account tooth bending deflection, fillet-foundation and contact deflection. Then, in order to verify the method′s validity, the calculation results of analytical modeling are compared with the simulation results of the dynamic meshing model with a finite element method. On this basis, when considering the time-varying mesh stiffness and shaft torsional stiffness, the dynamic stiffness matrix of a 1.5 MW wind turbine drive-train system is deduced and used to analyze the regular pattern of inherent characteristics and the sensitivity of the critical speed to the dynamic stiffness parameters. At the same time, it quantifies the critical speed fluctuation caused by changes in the dynamic stiffness amplitude. The results show that the instability of the critical speed of the drive-train system appears when the gear varying mesh stiffness fluctuates, and the critical speed of the rotor will increase since the amplitude of the time-varying stiffness is significantly higher. However, the critical speed of the drive-train system is insensitive to time-varying stiffness. This research can improve understanding of vibration characteristics and provide a reference for the optimal design of structures.