The growing number of traffic accidents in recent years has become a serious concern to society. Accidents caused by driver's drowsiness behind the steering wheel have a high fatality rate because of the marked decline in the driver's abilities of perception, recognition, and vehicle control abilities while sleepy. Preventing such accidents caused by drowsiness is highly desirable but requires techniques for continuously detecting, estimating, and predicting the level of alertness of drivers and delivering effective feedbacks to maintain their maximum performance. This paper proposes an EEG-based drowsiness estimation system that combines electroencephalogram (EEG) log subband power spectrum, correlation analysis, principal component analysis, and linear regression models to indirectly estimate driver's drowsiness level in a virtual-reality-based driving simulator. Our results demonstrated that it is feasible to accurately estimate quantitatively driving performance, expressed as deviation between the center of the vehicle and the center of the cruising lane, in a realistic driving simulator.