Fatigue driving is a major contributor to traffic accidents, as it reduces alertness and can even be fatal. To investigate alertness changes during prolonged driving, we first built a simulated driving experiment platform and designed an alertness detection experiment. Electroencephalogram (EEG) signals were collected during prolonged fatigue driving from 16 subjects. For each subject, the driving process was divided into eight stages from T0-T7. Then, the alertness level was analyzed by temporal complex network method based on multiplex limited penetrable visibility graphs from the collected EEG signals. The clustering coefficient, path length and global efficiency of the constructed complex network were extracted for each driving stage under five typical brain rhythms including delta, theta, alpha, beta, and gamma. The results indicate that after a long stage of driving, the clustering coefficient and path length show an overall increasing trend, while the global efficiency reveals an overall decreasing trend. Our findings may provide indicators for monitoring alertness level.