In this paper, the hysteresis characteristics of a transformer core are determined from limited on-line measured voltages and currents under certain excitations. A method for calculating the magnetization curve and hysteresis loops of the transformer core under various excitation is developed based on limited excitation conditions, and using the deep neural network, support vector regressor and the Wlodarski model. The coercivity and the amplitude of magnetic field strength of hysteresis loops can be captured with high accuracy based on this method. Then, a finite element model of the transformer core is constructed to predict the distributed magnetic flux density and the excitation current using the calculated hysteresis loops. The currents from various excitation voltages on two different transformer structures are also measured to compared with simulated currents. The outcome indicates that the overall hysteresis loops and magnetization curve of the transformer core may be useful for modeling the magnetic field and excitation current under any voltage excitation.