We describe driver behaviour and brain dynamics acquired from a 90-minute sustained-attention task in an immersive driving simulator. The data included 62 sessions of 32-channel electroencephalography (EEG) data for 27 subjects driving on a four-lane highway who were instructed to keep the car cruising in the centre of the lane. Lane-departure events were randomly induced to cause the car to drift from the original cruising lane towards the left or right lane. A complete trial included events with deviation onset, response onset, and response offset. The next trial, in which the subject was instructed to drive back to the original cruising lane, began 5-10 seconds after finishing the previous trial. We believe that this dataset will lead to the development of novel neural processing methodology that can be used to index brain cortical dynamics and detect driving fatigue and drowsiness. This publicly available dataset will be beneficial to the neuroscience and brain-computer interface communities.