Since current available sleep electroencephalogram data sets for sleep staging are all class imbalanced small data sets, it is hard to achieve ideal staging result by directly migration application of deep learning models. A deep automatic sleep staging model for class imbalanced small data sets was proposed, from the aspect of data oversampling and model training optimization. Firstly, a Modified Synthetic Minority Oversampling TEchnique (MSMOTE) was improved from the perspective of reducing the decision region, and the new technique was applied to generate the minority class samples in the original data sets. Then, the reconstructed class balanced data sets were used to pre-activate the sleep staging model. The 15-fold cross-validation experiment showed the overall classification accuracy was 86.73% and the macro-averaged F1-score was 81.70%. The value of F1 for the minimum class increased from 45.16% to 53.64% by using the data sets reconstructed by improved MSMOTE, to pre-activate the model. In conclusion, the model can realize the end-to-end learning for raw sleep electroencephalogram signals. It has a higher classification efficiency by comparison with recent advanced research and is suitable for the portable sleep monitors that work in conjunction with remote servers.