Abstract: The unbalanced magnetic pull(UMP)in a three-phase generator, caused by relative eccentricity, is calculated theoretically, and its effect on vibration of an eccentric rotor is studied. The air-gap permeance is expressed as a Fourier series. Then the UMP can be calculated by use of the Maxwell stress round either the rotor or stator surface and integration. The analytical expression of UMP for any pole-pair number is obtained and substituted into motion equation of system. The implicit nonlinear integer method- NEWMARK method is employed to solve the dynamic response of system under the UMP and eccentric mass force. Effects of relative eccentricity, rotor speed and pole number on the vibration of eccentric rotor are studied in detail.