A radial unbalanced magnetic pull (UMP) can be produced by an eccentric rotor and leads vibrations in large hydro-turbine generators. The influence of nonlinear UMP on the radial vibration of a large hydro-turbine generator is analyzed in this paper. The UMP is determined as a function of eccentricities and field currents by means of a simple analytical method instead of the finite element (FE) method. The analytical method employs the no-load characteristic curve of an electrical machine and saturation effects of the ferromagnetic materials are taken into consideration. FE rotor model of a large hydro-turbine generator unit, taking account of guide bearings, thrust bearing and periodic forces, is developed to investigate the influence of UMP on radial vibrations. The FE rotor model and the analytical method for UMP constitute the computational model. UMP is calculated under different rotor eccentricities and field currents by the proposed method. Comparing with other analytical methods, the effectiveness of the proposed method is verified. Dynamic responses of the FE model under different analytical methods for UMP are calculated to investigate the difference in vibration between different analytical methods. A simulated excitation test is performed and a comparative analysis between the calculated results and the field data is provided. The computational model is proved to be reasonable according to the analysis.