Cortical sources of resting state electroencephalographic (EEG) delta (2-4 Hz) and low-frequency alpha (8-10.5 Hz) rhythms show abnormal activity (i.e., current density) in patients with dementia due to Alzheimer's disease (AD). Here, we hypothesized that abnormality of this activity is related to relevant disease processes as revealed by cortical hypometabolism typically observed in AD patients by fluorodeoxyglucose positron emission tomography. Resting state eyes-closed EEG data were recorded in 19 AD patients with dementia and 40 healthy elderly (Nold) subjects. EEG frequency bands of interest were delta and low-frequency alpha. EEG sources were estimated in these bands by low-resolution brain electromagnetic tomography (LORETA). Fluorodeoxyglucose positron emission tomography images were recorded only in the AD patients, and cortical hypometabolism was indexed by the so-called Alzheimer's discrimination analysis tool (PALZ) in the frontal association, ventromedial frontal, temporoparietal association, posterior cingulate, and precuneus areas. Results showed that compared with the Nold group, the AD group pointed to higher activity of delta sources and lower activity of low-frequency alpha sources in a cortical region of interest formed by all cortical areas of the PALZ score. In the AD patients, there was a positive correlation between the PALZ score and the activity of delta sources in the cortical region of interest (p < 0.05). These results suggest a relationship between resting state cortical hypometabolism and synchronization of cortical neurons at delta rhythms in AD patients with dementia.