In this paper we propose a biometric solution for individual identification based on electroencephalography with classification using local probability centers. In our study, the electroencephalography signals of a subject are recorded from only one active channel Cz with eyes closed and without any external stimulations. The original signals are preprocessed by Haar wavelet transformation; then a number of features are extracted from the preprocessed signals; and then a classifier with local probability centers are employed to assign the signals to the right person according to the features extracted. By this method we have achieved an average identification accuracy of 96.21% for a dataset of 11 subjects' electroencephalography patterns and the high F-measure values of different persons has shown that this method performed robustly and effectively for various subjects. In addition, we have studied the variation of recognition accuracy with the time length of electroencephalography sessions and found that a longer electroencephalography session is usually more effective for individual identification. These results are in agreement to the previous research and show the evidence that the electroencephalography carries identity information and a longer electroencephalography session usually carries more identity information. With the simple implementation and good performance, we consider our proposed approach to be suitable for development and implementation in a 'unimodal' biometric identification system or may be combined with other biometric methods to form a 'multimodal' biometric identification system.