Electrostatic energy analyzers are irreplaceable instruments to analyze the electron beams energies. In this context, the knowledge of electron trajectories in electrostatic energy analyzers has major importance in collision physics as well as in different scientific instruments for surface science. In this study, electron trajectories for different energies in an ideal field 180 degrees hemispherical deflector analyzer are investigated by artificial neural network prediction method. The SIMION 8.1 simulation program is used as a data source for training and testing of artificial neural network. Artificial neural network based prediction has been performed using Matlab R2012b program. Obtained performance results indicate that this approach provides new perspectives for the rapid solution to the problems in charged particle optics.