The elastic support is an important component to support the wind power gearbox and absorb the dynamic load of the wind wheel. It is easy to be damaged during the operation of the wind turbine generator system, and its vibration response under the stable operation and variable speed and load conditions needs to be focused. Taking the drive train of a wind turbine generator system with 4MW two-point support as the research carrier, considering the flexibility of the elastic support of the wind turbine gearbox, the rigid-flexible coupling dynamic model of the drive train of the wind turbine generator system is established to study the vibration response of the elastic support under the stable operation of the drive train and variable speed and load conditions, and reveal the vibration characteristics of the elastic support under different working conditions. The results show that the axial vibration of elastic support is dominant when the main shaft is aligned, and the vibration space trajectory is elliptical; The misalignment of the main shaft sharply increases the axial vibration displacement of the elastic support, reaching the peak value 8.099mm at 0.1 ° deflection angle, and the radial displacement peak value caused by 0.05 ° deflection angle due to resonance; The bearing parameter analysis shows that the axial radial displacement of elastic bearing increases linearly with the increase of float bearing clearance, while the thrust bearing only affects the axial direction. Under variable speed and load condition, the vibration mode of elastic support in X/Y direction changes with the turbulence intensity, and the amplitude in Z-direction vibration displacement is related to the wind speed. Frequency-domain analysis shows that the vibration energy is concentrated on the rotational frequency 1 and 2 of the hub, and the coupling between the low frequency load transfer mechanism and the system mode significantly increases the fatigue risk of the elastic support.