For the purpose of modeling EEG signal which has nonstationary and nonlinear dynamic characteristics, this paper propose a state feedback real time recurrent neural network model. The state feedback real time recurrent neural network is structured to have memory structure in the state of hidden layers so that it has arbitrary dynamics and ability to deal with time-varying input through its own temporal operation. For the model test, Mackey-Glass time series is used as a nonlinear dynamic system and the model is applied to the prediction of three types of EEG, alpha wave, beta wave and epileptic EEG. Experimental results show that the performance of the proposed model is better than that of other neural network models which are compared in this paper in some view points of the converging speed in learning stage and normalized mean square error for the test data set.