This paper proposes a realistic model of magnetizing branches for transient calculation of electric power circuits. The model represents the nonlinear relationship between flux linkage and exciting current of magnetizing branches with a major loop and a family of minor loop trajectories, which has the capability of simulating the multi-valued hysteresis behavior. By applying the proposed model to transient calculation, an efficient algorithm is developed for obtaining the transient responses in electric power circuits. In the algorithm, the electric power circuit is divided into the magnetizing branches and the remaining linear part. The nonlinear differential equations are set up for the magnetizing branches and solved by the semi-explicit Runge–Kutta method. The transient calculation for the remaining linear part is performed on the basis of the solution to the magnetizing branches. Then, a laboratory measurement is made with a reduced-scale experimental arrangement. The measured results are compared with the calculated ones and a reasonable agreement is shown between them.