This paper proposes a new nonlinear broadband model of the power transformer which is both fit for steady state and transient simulation in power system. The model consists of high-frequency module and low-frequency module in parallel. Based on the black-box method, the high-frequency block is built in the form of π-type equivalent circuit, and the low-frequency block is in the form of conventional gamma-type circuit, in which core saturation characteristic is expressed by a nonlinear inductor. A power transformer is studied in the laboratory, simulations and experiments are carried out in case of power-frequency steady state, excitation currents distortions, lightning overvoltage, and very fast transient overvoltages (VFTO) respectively. The comparisons between the simulated and measured results verify the feasibility and validity of the model.