Sleep disorder is a serious public health problem. Unobtrusive home sleep quality monitoring system can better open the way of sleep disorder-related diseases screening and health monitoring. In this work, a sleep stage classification algorithm based on multiscale residual convolutional neural network (MRCNN) was proposed to detect the characteristics of electroencephalogram (EEG) signals detected by wearable systems and classify sleep stages. EEG signals were analyzed in each epoch of every 30 seconds, and then 5-class sleep stage classification, wake (W), rapid eye movement sleep (REM), and nonrapid eye movement sleep (NREM) including N1, N2, and N3 stages was outputted. Good results (accuracy rate of 92.06% and 91.13%, Cohen’s kappa of 0.7360 and 0.7001) were achieved with 5-fold cross-validation and independent subject cross-validation, respectively, which performed on European Data Format (EDF) dataset containing 197 whole-night polysomnographic sleep recordings. Compared with several representative deep learning methods, this method can easily obtain sleep stage information from single-channel EEG signals without specialized feature extraction, which is closer to clinical application. Experiments based on CinC2018 dataset also proved that the method has a good performance on large dataset and can provide support for sleep disorder-related diseases screening and health surveillance based on automatic sleep staging.