Grounding electrodes are essential in electrical power system to maintain a reliable operation, and to guarantee the safety of personnel and equipment. When a lightning strikes at a transmission tower, surge current waves travel to the foundations of the structure which are partially absorbed by the grounding impedance. As a consequence, the electrical potential increases in relation to a remote reference, which is named Grounding Potential Rising (GPR). These curves are very important to verify if the step voltages are in accordance with specific standards to guarantee a safety conditions during the transient state. In this paper, impedance of some grounding systems are calculated by classic models for a large frequency range, varying in different lengths and buried in homogeneous soils. Then, the GPR curves are by two recursive methods directly in time domain. These methods applies Vector Fitting technique on each grounding impedance response, where the poles and residues are obtained. Then, employing the recursive convolution and trapezoidal method, the GPR are computed directly in time domain. These curves are compared with the classic Numerical Laplace Transform (NLT) which have shown a good agreement with the recursive methods.