Multiscale entropy (MSE) was used to analyze electroencephalography (EEG) signals to differentiate patients with Alzheimer's disease (AD) from healthy subjects. It was found that the MSE values of the EEG signals from the healthy subjects are higher than those of the AD ones at small time scale factors in the MSE algorithm, while lower than those of the AD patients at large time scale factors. Based on the finding, we applied the linear discriminant analysis (LDA) to optimize the differentiating performance by comparing the resulting weighted sum of the MSE values under some specific time scales of each subject. The EEG data from 15 healthy subjects, 69 patients with mild AD, and 15 patients with moderate to severe AD were recorded. As a result, the weighted sum values are significantly higher for the healthy than the patients with moderate to severe AD groups. The optimal testing accuracy under five specific scales is 100% based on the EEG signals acquired from the T4 electrode. The resulting weighted sum value for the mild AD group is in the middle of those for the healthy and the moderate to severe AD groups. Therefore, the MSE-based weighted sum value can potentially be an index of severity of Alzheimer's disease.