In this paper, the authors use a non-uniform transmission line model, in which the per-unit length parameters (L(x,t), G(x,t), and C(x,t)) are dependent on space and time proposed by Yaqing Liu et al., to simulate the lightning-transient voltages of grounding systems. In this model, the electromagnetic coupling between different parts of grounding systems is taken into account and the influence of vertical rods on grounding grid is also considered. To solve telegrapher's equations of grounding systems, the authors propose a new numerical method that is developed from the MQ-FOM and is called to be the Radial Basis Function (RBF) - FDTD method. The RBF is used to find the finite difference approximations of spatial and temporal derivatives. In particular, with choosing the "optimal" shape parameter of the RBF, the result shows that the RBF-FDTD solution is better than the FDTD solution. Finally, the proposed method is very suitable for finding the solutions of telegraphy or EM coupling equations of all transmission lines in EMC problems with higher accuracy.