Distraction during driving has been recognized as a significant cause of traffic accidents. The aim of this study is to investigate Electroencephalography (EEG) -based brain dynamics in response to driving distraction. To study human cognition under specific driving tasks in a simulated driving experiment, this study utilized two simulated events including unexpected car deviations and mathematics questions. The raw data were first separated into independent brain sources by Independent Component Analysis. Then, the EEG power spectra were used to evaluate the time-frequency brain dynamics. Results showed that increases of theta band and beta band power were observed in the frontal cortex. Further analysis demonstrated that reaction time and multiple cortical EEG power had high correlation. Thus, this study suggested that the features extracted by EEG signal processing, which were the theta power increases in frontal area, could be used as the distracted indexes for early detection of driver inattention in real driving.