Loss of alertness can have dire consequences for people controlling motorized equipment or for people in professions such as defense. Electroencephalogram (EEG) is known to be related to alertness of the person, but due to high level of noise and low signal strength, the use of EEG for such applications has been considered to be unreliable. This study reports the fractal analysis of EEG and identifies the use of maximum fractal length (MFL) as a feature that is inversely correlated with the alertness of the subject. The results show that MFL (of only single channel of EEG) indicates the loss of alertness of the individual with mean (inverse) correlation coefficient = 0.82.