Sleep disorders seriously affect human health. Deep learning automatic sleep staging algorithms based on electroencephalograms (EEG) can assist experts in accurately diagnosing patients' sleep disorders. However, the imbalance in training data hinders the learning of minority class features, and due to the differences in data distribution, the accuracy of automatic sleep staging models trained on training data often decreases when applied to real-world data. To address this issue, we propose an unsupervised domain adaptation algorithm that combines class re-balancing strategies and semi-supervised learning. In particular, a balanced loss function is introduced to mitigate data imbalance issue in sleep staging datasets. Additionally, an average teacher method is designed, and random output interpolation and related confidence thresholding are introduced to improve the accuracy of pseudo-labels. The feature distribution of target domain data is optimized through a discriminator network, thereby improving the classification accuracy on the target domain. Experiments conducted on the SHHS, Sleep-EDF, and ISRUC-Sleep datasets demonstrate the effectiveness of the proposed algorithm. Compared to direct transfer, the accuracy improves by 3.28% to 13.27%. Compared to domain statistical alignment, the accuracy is increased by 6.73% to 14.52%. Compared to adaptive domain statistical alignment methods, the accuracy is increased by 0.78% to 5.82%.