This paper presents a high-precision Runge-Kutta (RK) method for solving transmission line equations. This method adopts high-order Taylor expansion in space, which improves the approximation accuracy of spatial differentiation. Compared with the traditional finite element time-domain method, when the number of samples per wavelength is the same, RK method has higher precision. At the same time, according to the Taylor model, researchers use RK method to solve transmission line equation in the external field excitation. The correctness and high precision of the RK method are verified by numerical examples of our study.