Detecting fatigue driving from electroencephalogram (EEG) signals constitutes a challenging problem of continuing interest since fatigue driving has caused the majority of traffic accidents. We carry out a simulated driving experiment for EEG data acquisition. Then, we calculate the wavelet entropy under the alert and fatigue state, respectively, and find that the wavelet entropy gets an acceptable performance on classification. Despite that the traditional entropy-based methods have been successfully applied to detect EEG-based fatigue driving, how to improve the classification remains to be investigated. To solve this problem, we in this paper propose a novel relative wavelet entropy complex network (RWECN) for improving the classification accuracy. In particular, we infer the complex network by regarding each EEG channel as a node and determining the connections of nodes in terms of the relative wavelet entropy between the EEG signals. Then, we extract a series of network statistical measures to characterize the topological structure of the brain networks. We combine the wavelet entropy and RWECN statistical measures to form a feature vector for realizing the classification of different states through the Fisher linear discriminant analysis. The results suggest that our method allows obtaining intrinsic and effective features from fatigue EEG signals and enables to improve the classification accuracy of EEG-based fatigue driving.