Patients in completely locked-in state (CLIS) due to amyotrophic lateral sclerosis (ALS) lose the control of each and every muscle of their body rendering them motionless and without any means of communication. Though some studies have attempted to develop brain-computer interface (BCI)-based communication methods with CLIS patients, little information is available of the neuroelectric brain activity of CLIS patients. However, because of the difficulties with and often loss of communication, the neuroelectric signature may provide some indications of the state of consciousness in these patients. We recorded electroencephalography (EEG) signals from 10 CLIS patients during resting state and compared their power spectral densities with those of healthy participants in fronto-central, central, and centro-parietal channels. The results showed significant power reduction in the high alpha, beta, and gamma bands in CLIS patients, indicating the dominance of slower EEG frequencies in their oscillatory activity. This is the first study showing group-level EEG change of CLIS patients, though the reason for the observed EEG change cannot be concluded without any reliable communication methods with this population.