In recent years, electroencephalogram (EEG) signals have gained significant popularity in the detection and recognition of drivers' unfavorable driving states (UDS) and related aspects. However, the methods that rely on traditional EEG features and evaluate different electrodes or brain regions separately have somewhat limited the further development of recognition effectiveness. To address this, this study analyzes the phase relationships between electrodes in EEG signals to reveal the functional networks and connectivity patterns within the brain. Three phase synchronization (PS) methods, namely phase locking value (PLV), corrected imaginary phase locking value (CIPLV), and weighted phase lag index (WPLI), are used to construct connectivity matrices and networks in six classic sub-rhythmic bands. Additionally, a 2D convolutional neural network (CNN) with fewer learning parameters is designed to automatically learn high-level abstractions and the most discriminative features, thereby avoiding the laborious and subjective process of manual feature extraction. The proposed method has been compared with traditional classification algorithms using a leave-one-out cross-validation strategy. The comparative results indicate that our proposed approach, which combines WPLI phase synchronization in the gamma1 sub-rhythmic band with a pyramid-structured CNN model, achieves significantly higher accuracy in recognizing drivers' UDS than other conventional methods through a one-way analysis of variance (ANOVA) followed by post hoc multiple comparisons with Tukey analysis. Furthermore, our proposed 2D-CNN model contains fewer parameters, making it more competitive for further practical applications in real-world driving scenarios.