This paper introduces a proper model for ferromagnetic core which includes hysteresis, saturation, eddy current losses, and anomalous losses. This model can generate symmetrical and asymmetrical loops with high accuracy. An artificial neural network is used to present the major dc hysteresis loop and initial magnetization curve based on a set of experimental data. This ferromagnetic core model is then used to estimate the inrush current of a single-phase transformer. Differential equations system obtained based on the equivalent circuit is converted into a nonlinear algebraic system of equations and then solved by Newton-Raphson routine. The predicted results are in good agreement with the experimental results.