Abstarct: Magnetic characteristics of the iron cores affect significantly the steady and transient performances of the transformers. Due to nonlinear and multi-values characteristics, modeling of the hysteresis behavior of a magnetic material is principally complicated. In general the conventional methods yield to inaccurate results, particularly when are employed to model a transient phenomena. Scalar model of Priesach is a powerful numerical method and might be applied for modeling of a transformer core with some confidences. However, programming the Priesach model coupled with external circuits of a transformer is somewhat complicated and needs a further considerations and proper less time-consuming computational algorithm. In this text, a comprehensive computerized model of a transformer core combined with winding details and electric equations of the terminals is presented. The numerical problems associated with implementation of the transformer model using Priesach model are reduced greatly by the suggested algorithm. That provides completed information regarding all electric and magnetic quantities of the transformer including the instantaneous voltages and currents, flux density and field intensity. Therefore by use of the proposed model, one can evaluate the steady state and transient performance of a transformer and specify for example the terminal parameters, degree of core saturation and the transformer contributing in the harmonics reducing.