Epilepsy is a worldwide common neurological condition where patients suffer from recurrent seizures, which are brief episodes of involuntary movement usually accompanied by loss of consciousness. To predict these events, researchers have analyzed the transition between two epileptic brain signals: interictal and pre-ictal. This work proposes to apply the NeuroEvolution of Augmenting Topologies (NEAT) as a neuroevolution approach to obtain optimal Spiking Neural Networks (SNNs) as a model to predict epileptic seizures. The CHB-MIT database, which collects brain epileptic signals obtained by the Electroencephalography (EEG) technique, was selected to test the model. The sensibility, specificity, and Seizure Prediction Horizon (SPH) metrics were used. The latter assesses the capacity to forecast an episode. The method showed competitive results, reaching mean values of 94.39% in sensibility, 81.65% in specificity, and 44.73 min in SPH, which are in the range of state-of-the-art proposals. Furthermore, our best and median results increased the SPH, achieving 50.34 and 48.10 min, respectively.