The apolipoprotein E (APOE) ε4 allele is a risk factor for Alzheimer’s disease (AD) that has been linked to changes in brain structure and function as well as to different biological subtypes of the disease. The present study aimed to investigate the association of APOE ε4 genotypes with brain functional impairment, as assessed by quantitative EEG (qEEG) in patients on the AD continuum. The study population included 101 amyloid positive patients diagnosed with mild cognitive impairment (MCI) (n = 50) and AD (n = 51) that underwent resting-state EEG recording and CSF Aβ42 analysis. In total, 31 patients were APOE ε4 non-carriers, 42 were carriers of one, and 28 were carriers of two APOE ε4 alleles. Quantitative EEG analysis included computation of the global field power (GFP) and global field synchronization (GFS) in conventional frequency bands. Amyloid positive patients who were carriers of APOE ε4 allele(s) had significantly higher GFP beta and significantly lower GFS in theta and beta bands compared to APOE ε4 non-carriers. Increased global EEG power in beta band in APOE ε4 carriers may represent a brain functional compensatory mechanism that offsets global EEG slowing in AD patients. Our findings suggest that decreased EEG measures of global synchronization in theta and beta bands reflect brain functional deficits related to the APOE ε4 genotype in patients that are on a biomarker-verified AD continuum.