In this paper a new approach to the electroencephalogram (EEG) signal simulation based on the artificial neural networks (ANN) is proposed. The aim was to simulate the spontaneous human EEG background activity based solely on the experimentally acquired EEG data. Therefore, an EEG measurement campaign was conducted on a healthy awake adult in order to obtain an adequate ANN training data set. As demonstration of the performance of the ANN based approach, comparisons were made against autoregressive moving average (ARMA) filtering based method. Comprehensive quantitative and qualitative statistical analysis showed clearly that the EEG process obtained by the proposed method was in satisfactory agreement with the one obtained by measurements.