Sleep disorder is a symptom of many neurological diseases that may significantly affect the quality of daily life. Traditional methods are time-consuming and involve the manual scoring of polysomnogram (PSG) signals obtained in a laboratory environment. However, the automated monitoring of sleep stages can help detect neurological disorders accurately as well. In this study, a flexible deep learning model is proposed using raw PSG signals. A one-dimensional convolutional neural network (1D-CNN) is developed using electroencephalogram (EEG) and electrooculogram (EOG) signals for the classification of sleep stages. The performance of the system is evaluated using two public databases (sleep-edf and sleep-edfx). The developed model yielded the highest accuracies of 98.06%, 94.64%, 92.36%, 91.22%, and 91.00% for two to six sleep classes, respectively, using the sleep-edf database. Further, the proposed model obtained the highest accuracies of 97.62%, 94.34%, 92.33%, 90.98%, and 89.54%, respectively for the same two to six sleep classes using the sleep-edfx dataset. The developed deep learning model is ready for clinical usage, and can be tested with big PSG data.