We applied Lempel-Ziv complexity (LZC) combined with brain electrical activity mapping (BEAM) to study the change of alertness under sleep deprivation in our research. Ten subjects were involved in 36 hours sleep deprivation (SD), during which spontaneous electroencephalogram (EEG) experiments and auditory evoked EEG experiments-Oddball were recorded once every 6 hours. Spontaneous and evoked EEG data were calculated and BEAMs were structured. Results showed that during the 36 hours of SD, alertness could be divided into three stages, i.e. the first 12 hours as the high stage, the middle 12 hours as the rapid decline stage and the last 12 hours as the low stage. During the period SD, LZC of Spontaneous EEG decreased over the whole brain to some extent, but remained consistent with the subjective scales. By BEAMs of event related potential, LZC on frontal cortex decreased, but kept consistent with the behavioral responses. Therefore, LZC can be effective to reflect the change of brain alertness. At the same time LZC could be used as a practical index to monitor real-time alertness because of its simple computation and fast calculation.