A Meshless Time Domain Method is used in the local support domain to solve Maxwell's equations for one-dimensional transient electromagnetic problems. The approach is based on a combination of the Meshless Radial Basis Functions and the Leapfrog time-stepping scheme for the Finite-Difference approximation of the first order partial derivatives. A comparison is performed between the conventional FDTD and RBF's with Gaussian, Wendland-C4 Compactly Supported RBF (CSRBF) and Inverse Multi-Quadric (IMQ) basis functions. The numerical results showed that the proposed method provides an accurate solution for transient electromagnetic problems.