Abstract: High-quality sleep is linked with physical development, cognitive function, learning, and attention in children. Since early symptoms of sleep disorders in children are not obvious and require long-term monitoring, there is an urgent need to develop a method for monitoring children’s sleep that can prevent and diagnose these disorders in advance. Polysomnography (PSG) is the basic test for sleep disorders recommended by clinical guidelines. Sleep quality can be assessed and sleep disorders can be identified by observing the changes in patterns of PSG during each sleep period. Sleep staging in children was researched and single-channel electroencephalogram (EEG) signals recorded by PSG was used in this study. On the basis of Alexnet, we use a one-dimensional convolutional neural network (1D-CNN) model instead of a two-dimensional model to propose a 1D-CNN structure composed of five convolutional layers, three pooling layers, and three fully connected layers, as well as a batch normalization layer to 1D-CNN while keeping the size of the convolutional kernel constant. Moreover, the dataset was augmented with an overlapping method to address its small size. The experimental results showed that the accuracy of this model for children’s sleep staging was 84.3%. According to the normalized confusion matrix obtained from the PSG data of Beijing Children’s Hospital, the classification performance of wake, N2, N3, and REM stages of sleep was very good. Because stage N1 sleep was misclassified as wake, N2, and REM sleep in some cases, future research should focus on improving the accuracy of stage N1 sleep. Overall, the 1D-CNN model proposed in this paper can realize automatic sleep staging for children based on single-channel EEG with sleep stage markers. In the future, more research is needed to develop a more suitable sleep staging strategy for children and to conduct experiments with a larger amount of data.