Driver distraction has been recognized as a significant cause of traffic incidents. Therefore, the aim of this study was to investigate Electroencephalography (EEG) dynamics in response to distraction during driving. To study human cognition under specific driving task, we used Virtual Reality (VR) based driving simulation to simulate events including unexpected car deviations and mathematics questions (math) in real driving. For further assessing effects of the stimulus onset asynchrony (SOA) between the deviation onset and math presented on the EEG dynamics, we designed five cases with different SOA. The scalp-recorded EEG channel signals were first separated into independent brain sources by Independent Component Analysis (ICA). Then, the Event-Related-Spectral-Perturbations (ERSP) measuring changes of EEG power spectra were used to evaluate the brain dynamics in time-frequency domains. Results showed that increases of theta band (5-7.8 Hz) and beta band (12.2-17 Hz) power were observed in the frontal cortex. Results demonstrated that reaction time and multiple cortical EEG sources responded to the driving deviations and math occurrences differentially in the stimulus onset asynchrony. Results also suggested that the theta band power increase in frontal area could be used as the distracted indexes for early detecting driver's inattention in the future.