This work presents a transmission line model for simulating electromagnetic transients directly in the time domain. For this purpose, the exact equivalent π-circuit is used, which represents the line taking into account its distributed and frequency-dependent parameters. The admittances that constitute the exact equivalent π-circuit are approximated by rational functions using the vector fitting technique. Then, for each admittance, an electrical circuit is synthesized, consisting of an association of discrete elements (resistors, inductors, and capacitors) aiming at modeling the transmission line, thus allowing its use in any circuit simulation software and the eventual connection of nonlinear elements. From the simulation results, it is reasonable to state that the proposed model is a feasible representation, which aggregates the same features of the exact equivalent π-circuit directly in the time domain, not only in steady state, but mainly during transients and also without the need for using convolutions, as well as inverse Laplace or Fourier transforms.