Driver drowsiness is considered to be a very critical issue causing many fatal accidents, injuries and property damages. Therefore, it has been an area of intensive research in recent years. In this paper, a driving simulator based study was conducted to observe the significant changes that occur in the EEG power spectrum during monotonous driving. Nine healthy university students voluntarily participated in the experiment. The absolute band power of the EEG signal was computed by taking the FFT of the time series signal and then the power spectral density was computed using Welch method. Our findings conclude that alpha and theta band powers increase significantly (p<0.05) when a subject moves from alert state to drowsy state. These changes are more dominant in the occipital and parietal regions when compared to the other regions. The findings of this study provide a promising drowsiness indicator which can be used to prevent road accidents caused by driver drowsiness.