The detection of pilots' mental states is critical, as abnormal mental states have the potential to cause catastrophic accidents. This study demonstrates the feasibility of using deep learning techniques to classify different fatigue levels, specifically a normal state, low fatigue, and high fatigue. To the best of our knowledge, this is the first study to classify fatigue levels in pilots. Our approach employs the hybrid deep neural network comprising five convolutional blocks and one long short-term memory block to extract the significant features from electroencephalography signals. Ten pilots participated in the experiment, which was conducted in a simulated flight environment. Compared to four conventional models, our proposed model achieved a superior grand-average accuracy of 0.8801, outperforming other models by at least 0.0599 in classifying fatigue levels. In addition to successfully classifying fatigue levels, our model provided valuable feedback to subjects. Therefore, we anticipate that our study will make the significant contributions to the advancement of autonomous flight and driving technologies, leveraging artificial intelligence in the future.