Using a smart method for automatic diagnosis in medical applications, such as sleep stage classification is considered as one of the important challenges of the last few years which can replace the time-consuming process of visual inspection done by specialists. One of the problems regarding the automatic diagnosis of sleep patterns is extraction and selection of discriminative features generally demanding high computational burden. This paper provides a new single-channel approach to automatic classification of sleep stages from EEG signal. The main idea is to directly apply the raw EEG signal to deep convolutional neural network, without involving feature extraction/selection, which is a challenging process in the previous literature. The proposed network architecture includes 9 convolutional layers followed by 2 fully connected layers. In order to make the samples of different classes balanced, we used a preprocessing method called data augmentation. The simulation results of the proposed method for classification of 2 to 6 classes of sleep stages show the accuracy of 98.10%, 96.86%, 93.11%, 92.95%, 93.55% and Cohen’s Kappa coefficient of 0.98%, 0.94%, 0.90%, 0.86% and 0.89%, respectively. Furthermore, comparing the obtained results with the state-of-the-art methods reveals the performance improvement of the proposed sleep stage classification in terms of accuracy and Cohen’s Kappa coefficient.