Based on conventional drive train model of wind turbines, a planetary gearbox with flexible supporting between gearbox case and nacelle base is considered, and the coupled dynamic model of the drive train system is derived. The gearbox inner vibration performances are evaluated under different flexible parameters by means of dynamic simulation. It is shown that natural frequencies of each shaft are drifting while damping and elastic coefficients changing. Analysis also reveals that the flexible supporting mitigates torsion vibrations of each shaft. To minimizing torsion vibrations, a new searching approach is used to find out optimal parameters of the flexible supporting. Simulation results show that dynamic torque loads of the drive train are reduced, which is useful to wind turbine structure design.