Sleep scoring is one of the primary tasks for the classification of sleep stages in Electroencephalogram (EEG) signals. Manual visual scoring of sleep stages is time-consuming as well as being dependent on the experience of a highly qualified sleep expert. This paper aims to address these issues by developing a new method to automatically classify sleep stages in EEG signals. In this research, a robust method has been presented based on the clustering approach, coupled with probability distribution features, to identify six sleep stages with the use of EEG signals. Using this method, each 30-second EEG signal is firstly segmented into small epochs and then each epoch is divided into 60 sub-segments. Each sub-segment is decomposed into five levels by using a discrete wavelet transform (DWT) to obtain the approximation and detailed coefficient. The wavelet coefficient of each level is clustered using the k-means algorithm. Subsequently, features are extracted based on the probability distribution for each wavelet coefficient. The extracted features then are forwarded to the least squares support vector machine classifier (LS-SVM) to identify sleep stages. Comparisons with several existing methods are also made in this study. The proposed method for the classification of the sleep stages achieves an average accuracy rate of 97.4%. It can be an effective tool for sleep stages classification and can be useful for doctors and neurologists for diagnosing sleep disorders.