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Alzheimer’s disease (AD) is the most prevalent cause of dementia, being considered a major health problem, especially in developed countries. Late-onset AD is the most common form of the disease, with symptoms appearing after 65 years old. Genetic determinants of AD risk are vastly unknown, though, <inline-formula> <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math> </inline-formula>4 allele of the <i>ApoE</i> gene has been reported as the strongest genetic risk factor for AD. The objective of this study was to analyze the relationship between brain complexity and the presence of <i>ApoE</i><inline-formula> <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math> </inline-formula>4 alleles along the AD continuum. For this purpose, resting-state electroencephalography (EEG) activity was analyzed by computing Lempel-Ziv complexity (LZC) from 46 healthy control subjects, 49 mild cognitive impairment subjects, 45 mild AD patients, 44 moderate AD patients and 33 severe AD patients, subdivided by <i>ApoE</i> status. Subjects with one or more <i>ApoE</i><inline-formula> <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math> </inline-formula>4 alleles were included in the carriers subgroups, whereas the <i>ApoE</i><inline-formula> <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math> </inline-formula>4 non-carriers subgroups were formed by subjects without any <inline-formula> <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math> </inline-formula>4 allele. Our results showed that AD continuum is characterized by a progressive complexity loss. No differences were observed between AD <i>ApoE</i><inline-formula> <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math> </inline-formula>4 carriers and non-carriers. However, brain activity from healthy subjects with <i>ApoE</i><inline-formula> <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math> </inline-formula>4 allele (carriers subgroup) is more complex than from non-carriers, mainly in left temporal, frontal and posterior regions (<i>p</i>-values < 0.05, FDR-corrected Mann–Whitney <i>U</i>-test). These results suggest that the presence of <i>ApoE</i><inline-formula> <math display="inline"> <semantics> <mi>ε</mi> </semantics> </math> </inline-formula>4 allele could modify the EEG complexity patterns in different brain regions, as the temporal lobes. These alterations might be related to anatomical changes associated to neurodegeneration, increasing the risk of suffering dementia due to AD before its clinical onset. This interesting finding might help to advance in the development of new tools for early AD diagnosis.