Alzheimer’s disease (AD) is a brain pathology that leads to a progressive loss of cognitive functions. In its first stage, it is often mistaken for normal aging because the symptoms are not severe. This condition is referred as Mild Cognitive Impairment (MCI). Electroencephalography (EEG) has been widely used for investigating AD. In particular, the resolution of the so-called EEG inverse problem allows you to reconstruct the distribution of brain active sources. Standard EEG is characterized by a low spatial resolution that can be improved by increasing the number of the recording sensors (HD-EEG). The purpose of this paper is the computation of the brain electrical activity by the eLORETA method for three groups of subjects: CNT (healthy subjects), MCI patients and AD patients. The novelty of this work is that eLORETA was applied to HD-EEG. The hallmark of AD is the shift of the EEG power spectrum to lower frequencies. The analysis of the results suggests that EEG of MCI and, even more, of AD is characterized by an increasing power in delta and theta bands as compared with CNT. Moreover, it has been shown that the greater source activation involves Brodmann areas typically affected by this pathology and is consistent with it. eLORETA shows the involved Brodmann areas automatically.