Fatigue, one of the most important factors affecting road safety, has attracted many researchers’ attention. Most existing fatigue detection methods are based on feature engineering and classification models. The feature engineering is greatly influenced by researchers’ domain knowledge, which will lead to a poor performance in fatigue detection, especially in cross-subject experiment design. In addition, fatigue detection is often simplified as a classification problem of several discrete states. Models based on deep learning can realize automatic feature extraction without the limitation of researcher’s domain knowledge. Therefore, this paper proposes a regression model combined convolutional neural network and recurrent neural network for electroencephalogram-based (EEG-based) cross-subject fatigue detection. At the same time, a twofold random-offset zero-overlapping sampling method is proposed to train a bigger model and reduce overfitting. Compared with existing results, the proposed method achieves a much better result of 0.94 correlation coefficient (COR) and 0.09 root mean square error (RMSE) in a within-subject experiment design. What is more, there is no misclassification between awake and drowsy states. For cross-subject experiment design, the COR and RMSE are 0.79 and 0.15, respectively, which are close to the existing within-subject results and better than similar cross-subject results. The cross-subject regression model is very important for fatigue detection application since the fatigue indication is more precise than several discrete states and no model calibration is required for a new user. The twofold random-offset zero-overlapping sampling method can also be used as a reference by other EEG-based deep learning research.