Sleep is a natural phenomenon controlled by the central nervous system. The sleep-wake pattern, which functions as an essential indicator of neurophysiological organization in the neonatal period, has profound meaning in the prediction of cognitive diseases and brain maturity. In recent years, unobtrusive sleep monitoring and automatic sleep staging have been intensively studied for adults, but much less for neonates. This work aims to investigate a novel video-based unobtrusive method for neonatal sleep-wake classification by analyzing the behavioral changes in the neonatal facial region. A hybrid model is proposed to monitor the sleep-wake patterns of human neonates. The model combines two algorithms: deep convolutional neural network (DCNN) and support vector machine (SVM), where DCNN works as a trainable feature extractor and SVM as a classifier. Data was collected from nineteen Chinese neonates at the Children's Hospital of Fudan University, Shanghai, China. The classification results are compared with the gold standard of video-electroencephalography scored by pediatric neurologists. Validations indicate that the proposed hybrid DCNN-SVM model achieved reliable performances in classifying neonatal sleep and wake states in RGB video frames (with the face region detected), with an accuracy of 93.8 ± 2.2% and an F1-score 0.93 ± 0.3.