In this article, theoretical derivation and numerical simulating calculation are used for the analysis of the unbalanced magnetic pull (UMP) and the vibration characteristics caused by the radial air-gap eccentric in the generator. Firstly, the magnetic flux density under normal condition, static air-gap eccentricity, dynamic air-gap eccentricity, and mixed air-gap eccentricity, are analyzed. Then the UMP formulas for normal condition and each air-gap eccentricity fault are deduced to investigate the exciting characteristics and the vibration response features. Finally, the SDF-9 Non-salient Pole Synchronous Generator model is built in Ansoft Maxwell to calculate the detailed UMP data for the comparison with the theoretical analysis and the experiment results. Generally, the theoretical analysis, the simulation data, and the experimental result are consistent with each other. It is shown that the static air-gap eccentricity will cause rotor UMP at 2f (f is the mechanical frequency) and bring in 2nd harmonic vibrations. However, there are two cases for the dynamic air-gap eccentricity, i.e., the composite force is zero and not zero, of which the latter one will be primary the fundamental-frequency UMP. In the case of mixed air-gap eccentricity, 1st and 2nd harmonic rotor UMP will both be induced (considering the composite force is not zero). As the air-gap eccentricity develops, UMP will be also increased.