The transient response behavior of a transmission line system with frequency-varying loads is one of the key issues in the field of electromagnetic compatibility, and it is closely related to the overall working state of the equipment. However, when the load is composed of frequency-varying networks made of capacitors, inductors, and other components, it is quite difficult to directly analyze the transient response of the transmission line under electromagnetic pulse excitation. In this paper, the transmission line is modeled based on the Agrawal model. By constructing a set of equations describing the transient response characteristics of frequency-varying network loads using state variable equations, the transient response of the transmission line system under lumped excitation sources is solved. The Finite-Difference Time-Domain(FDTD) method is employed to calculate the excitation field around the transmission line, and an equivalent excitation voltage source is introduced into the Agrawal model to complete the analysis of the transient behavior of the transmission line inside the cavity under external field excitation. The calculation results verify the feasibility, efficiency, and accuracy of the proposed method.