In order to solve nonlinear system torsion response of turbo-generator unit, an increment transfer matrix method based on step-by-step integration method and traditional transfer matrix method was put forward. The method can be directly used to analyze nonlinear differential equations. Combined with Riccati method, the increment transfer matrix method was used in a multi-mass model. And matrix equations calculating the responses of torsional vibrations were deduced. Torsional vibration resulted from the faults of short circuit and asynchronous synchronization of 600MW steam turbo-generator unit were discussed in this work by using the increment transfer matrix method which can also extend the application of transfer matrix method in nonlinear field.