Preventing accidents due to drowsiness at the wheel has been an area of extensive research in the past few years because of the severity of the problem. For this purpose, continuous observation of physiological signals of the driver provides the possibility of detecting drowsiness. A simulator based study is conducted to evaluate driver drowsiness using electroencephalographic (EEG) signal. Twenty two healthy subjects voluntarily participated in the experiment. Relative power of each EEG frequency band is computed by taking the FFT of time domain signal using Welch's method to observe the spectral variation from alert to drowsy state. Topographic maps are used to visualize the spectral changes that occur in each power band. Results show that the relative power of theta and alpha bands exhibit significant changes in drowsy state and these changes are more dominant in the occipital and parietal regions of the brain.