Transient response analysis of Transmission Line(TL) systems with frequency-dependent load is an important topic in the field of electromagnetic compatibility, especially for the situation where the frequency-dependent network is more complicated or the internal structure is not clear, the corresponding analysis of its transient response is more difficult. In this paper, firstly, the corresponding sampling values are obtained by measuring or calculating the admittances of the frequency-dependent loads at the sampling frequencies, and the equivalence of the admittances is performed by adopting the rational function approximation; then, the Piecewise Linear Recursive Convolution(PLRC) expression of the voltage at the connection point between the TL and frequency-dependent loads is obtained by bringing the poles and residues solved by Matrix Pencil Method(MPM) into the PLRC technique; finally,the transient response analysis of the TL system with frequency-dependent loads is obtained by combining the MPM, PLRC and TL equation, and the performance of the proposed method is verified by two numerical examples. The results illustrate that the proposed method has obvious advantages in calculation accuracy.