The mental state of a driver can be accurately and reliably evaluated by detecting the driver's electroencephalogram (EEG) signals. However, traditional machine learning and deep learning methods focus on the single electrode feature analysis and ignore the functional connection of the brain. In addition, the recent brain function connection network method needs to manually extract substantial brain network features, which results in cumbersome operation. For this reason, this paper introduces graph convolution combined with brain function connection theory into the study of mental fatigue and proposes a method for driving fatigue detection based on the partial directed coherence graph convolutional neural network (PDC-GCNN), which can analyze the characteristics of single electrodes while automatically extracting the topological features of the brain network. We designed a fatigue driving simulation experiment and collected the EEG signals. In the present work, the PDC method constructs the adjacency matrix to describe the relationship between EEG channels, and the GCNN combines single-electrode local brain area information and brain area connection information to further improve the performance of detecting fatigue states. Based on the features of differential entropy (DE) and power spectral density (PSD), the average recognition accuracy of ten-fold cross validation is 84.32% and 83.84%, respectively. For further experiments on each subject, the average recognition results are 95.24%/5.10% (PSD) and 96.01%/3.81% (DE). This research can be embedded in the vehicle driving fatigue detection system, which has practical application value.