Electroencephalogram (EEG) analysis has been widely used in disease diagnosis. The EEG detection of the patients with epilepsy can be used to make judgments about patients' conditions in time, which is of great practical value. Therefore, the techniques of automatic detection, diagnosis and classification of epileptic EEG signals are urgently needed. In order to realize fast and accurate automatic detection and classification of the EEG signals during the normal, interictal and ictal periods of epilepsy, we propose an automatic classification and recognition method which combines the Real Adaboost algorithm based on error-correcting output codes (ECOC) with a feature extraction method based on sample entropy (SampEn) and wavelet packet energy in this paper. In the present study, we used the sample entropy of input signals and the energy of some parts of frequency bands as features, and then we classified the extracted features with the method combining ECOC with Real AdaBoost algorithm. In order to test the validity, we used the epilepsy database from the University of Bonn. The database has 5 groups of EEG signals, which contains the data of normal people with their eyes open or closed, the data collected inside and outside of the epileptic foci from patients during their interictal period and the data from patients during their ictal period. The results showed that the method had strong abilities of classification and recognition of the EEG signals, and especially the recognition rate had been improved significantly. The average recognition rate of the EEG signals with different features during the three periods of the five groups mentioned above can reach 96.78%, which is superior to those with algorithms recorded in many other literatures. The method has better stability, processing speed and potential of real-time application, and it plays a supporting role in the prediction and detection of epilepsy in clinical practice.