In this paper, weighted-permutation entropy (WPE) is applied to investigating the complexity abnormalities of Alzheimer's disease (AD) by analyzing 16-channel electroencephalograph (EEG) signals from 14 severe AD patients and 14 age-matched normal subjects. The WPE values are estimated in the delta, the theta, the alpha, and the beta sub-bands for each channel with an overlapped sliding window. WPE is modified from the permutation entropy (PE), which has been recently suggested as a measurement to extract the complexity of the EEG signals. The advantage of WPE over PE is verified by both the model simulated and the experimental EEG signals. Although the results show that both the average PE and WPE of AD patients are decreased in contrast with the normal group in these four sub-bands, especially in the theta band, WPE can exhibit a better performance in distinguishing the AD patients from the normal controls by the more significant differences in the four sub-bands, which may be attributed to the brain dysfunction. Thus, it suggests that WPE may become a probable useful tool to detect brain dysfunction in AD and it seems to be promising to disclose the abnormalities of brain activity for other neural disease.