The air-cooled turbo-generator often works in the more frequent start-up and shut-down operation. Either the misoperation or the failure of synchronizing controllers can cause the out of phase synchronization fault. The fault can disturb the power angle and cause a strong impact electromagnetic force for the generator. With the traditional numerical calculation method, it is difficult to calculate the variations of key physical parameters and the electromagnetic field in the end region of the generator under complex working conditions, especially the out of phase synchronization fault. In order to solve the problem, a calculation method of the nonlinear transient electromagnetic field with multi-domain field-circuit-grid coupled is proposed. The correctness of the model and method is validated by comparing the calculated and test values of the magnetic density flux at the key points of the generator under the no-load condition. Based on this method, the power angle variation, the magnetic flux leakage distribution in the end region, and the electromagnetic force on the end winding in the transient process of the fault are calculated and analyzed.