Human performances are reported to decrease during the period of sleep-to-wake transition, which is called sleep inertia. Lack of awareness of the performance impairment during this state may lead us to make mistakes, especially during driving. This study aims to investigate the difference in the electroencephalography (EEG) signals between alert and sleep inertia during eyes-closed condition based on fractal dimension and examine the differences between Fz, Cz, Pz, FCz and Oz. Nine healthy subjects had performed two sessions of the experiment; alert and sleep inertia. To obtain the sleep inertia state, subjects were needed to sleep in the provided room and the EEG signals were recorded and monitored by the researcher. Subjects were awakened from sleep after they reached the stage 3 of the first cycle of sleep for five minutes to reduce the inter-individual variation in the EEG signal. Each EEG signal were analyzed based on its fractal dimension estimated using Higuchi's algorithm. A kmax parameter of 80 has been selected for analyzing every 60 seconds of the signal with 512 Hz sampling rate. To support this analysis, a power spectrum of each signal was obtained and the correlation with the fractal dimension can be determined. The differences of fractal dimension and power spectrum between alert and sleep inertia state have been tested statistically using t-test. Fractal dimension estimated in sleep inertia EEG signal was higher than alert state and there were significant differences at Fz. Based on spectrum power, delta, theta and alpha power showed a significant difference at Fz and FCz. The significant difference of fractal dimension and delta, theta and alpha power found at Fz and FCz during eyes closed may be associated with the impairment of subject performances which related to the brain regions' functions. © 2018 IEEE.