Nowadays, artificial intelligence is widely used in many biomedical-oriented problems. Because of obtained effective and efficient results, the use of intelligent solution mechanisms by artificial intelligence techniques is mainly focused on healthcare applications. Moving from the explanations, the objective of this paper is to provide an adaptive neuro-fuzzy inference system (ANFIS) trained by a recent optimization algorithm: electro-search optimization (ESO) for predicting the electroencephalogram (EEG) time series. In detail, the research was directed to the EEG time series showing chaotic characteristics so that an effective hybrid system can be designed for having an idea about future states of human brain activity in the case of possible diseases. The developed ANFIS-ESO system was evaluated with five different EEG time series and the obtained findings were reported accordingly. In addition, the ANFIS-ESO system was compared with alternative techniques-systems in order to see the performances according to different systems. In the end, it is possible to mention that the ANFIS-ESO system provides well-enough results in terms of predicting EEG time series. As a result of encouraging results, ANFIS-ESO is currently used actively for real cases.