Due to grid fault, the fluctuation of electromagnetic torque can lead to the torsional vibration fatigue loss of wind turbine shaft system. In severe cases, it can damage the shaft. It is necessary to investigates the torsional vibration responses of drive chain and its influence on key components under different grid faults. First of all, a four-mass model considering the flexible wind turbine transmission chain is established by using the centralized quality method. The torsional vibration characteristics of the transmission chain of the wind turbine are analyzed by modal analysis. Secondly, in order to characterize the influence of different fault types on the torsional vibration of the drive train shaft of wind turbines, based on the electromagnetic transient model of doubly-fed generator, the expressions of electro-magnetic torque under symmetrical and unsymmetrical faults of the power grid are deduced. Finally, based on the 4-mass transmission chain model, the influences of single-phase, two-phase and three-phase earth fault on the torsional vibration transmission of the transmission chain are simulated and analyzed. The results of show that different kinds of power grid faults will affect the torsional frequency of different transmission chains and different key components. The torsional vibration amplitudes of transmission chains caused by three-phase grounding grid faults are high, and high-speed axis mass Inter-torsional torque can more fully reflect the torsional vibration frequency, and the generator components are more affected by grid faults.