Sleep disorder is a serious public health problem. Non hospital sleep monitoring system for monitoring sleep quality can effectively support the screening of sleep disorder related diseases. A new algorithm of multi-scale residual convolutional neural network (MS-RESCNN) was proposed to discover the feature of electroencephalography (EEG) signals detected with wearable system and staging the sleep stage. EEG signals were analyzed by this algorithm every 30 seconds, and then sleep staging results of wake-up (W), rapid eye movement sleep (REM) and non-rapid eye movement sleep (NREM) were outputed. NREM can also be subdivided into N1, N2 and N3 stages. 5-fold cross validation and independent subject cross validation were performed on the dataset with Kappa cofficients 0.7360 and 0.7001, respectively. The accuracy rates of those methods were 92.06% and 91.13%, respectively. Compared with the other methods, our proposed method can obtain the information of sleep stages from single channel EEG signals without special feature extraction. It has a good performance and can provide support for clinical application based on automatic sleep staging.