In this paper, a new detailed analytical model of a salient-pole synchronous generator (SPSG) under dynamic eccentricity (DE) is presented which is capable of accounting for the effects of magnetic saturation, rotor pole shoe saliency, and space distribution of stator phases and rotor winding. A real form of rotor pole shoes is taken into account in the proposed SPSG air-gap function distribution. Saturation effects incorporate into the air-gap function of SPSG as a simple proposed analytic equation that varies by the generator load and operating condition. Furthermore, variation of the resulted air-gap distribution of SPSG in the presence of DE fault is then computed precisely and the inverse air-gap function calculated using Fourier series in order to compute time varying self- and mutual-inductances of stator phases and rotor winding via the modified winding function approach (MWFA). The computed inductances are used for simulation of SPSG and studying the frequency spectrum of stator line current in the presence of DE fault. It is shown that the results of proposed model are closer to the finite-element (FE) computation results compared to the available analytic models.