Sleep is an essential part of human life, and the quality of one's sleep is also an important indicator of one's health. Analyzing the Electroencephalogram (EEG) signals of a person during sleep makes it possible to understand the sleep status and give relevant rest or medical advice. In this paper, a decent amount of artificial data generated with a data augmentation method based on Discrete Cosine Transform from a small amount of real experimental data of a specific individual is introduced. A classification model with an accuracy of 92.85% has been obtained. By mixing the data augmentation with the public database and training with the EEGNet, we obtained a classification model with significantly higher accuracy for the specific individual. The experiments have demonstrated that we can circumvent the subject-independent problem in sleep EEG in this way and use only a small amount of labeled data to customize a dedicated classification model with high accuracy.