Automatic sleep stage classification is vital for evaluating the quality of sleep. Conventionally, sleep is monitored using multiple physiological sensors that are uncomfortable for long-term monitoring and require expert intervention. In this study, we propose an automatic technique for multi-stage sleep classification using photoplethysmographic (PPG) signal. We have proposed a convolutional neural network (CNN) that learns directly from the PPG signal and classifies multiple sleep stages. We developed models for two- (Wake-Sleep), three- (Wake-NREM-REM) and four- (Wake-Light sleep-Deep sleep-REM) stages of sleep classification. Our proposed approach shows an average classification accuracy of 94.4%, 94.2%, and 92.9% for two, three, and four stages, respectively. Experimental results show that the proposed CNN model outperforms existing state-of-the-art models (classical and deep learning) in the literature.