Allele 4 of the apolipoprotein E gene (APOE ε4) and hypertension are considered risk factors for Alzheimer’s Disease (AD). The detection of differences in cognitive function and brain networks between hypertensive patients who are APOE ε4 carriers and non-carriers may help in understanding how hypertension and risk genes cumulatively impair brain function, which could provide critical insights into the genetic mechanism by which hypertension serves as a potential risk factor for cognitive decline and even AD. Using behavioral data from 233 elderly hypertensive patients and neuroimaging data from 38 of them from Beijing, China; the study aimed to assess the effects of APOE ε4 on cognition and to explore related changes in functional connectivity. Cognitively, the patients with APOE ε4 showed decreased executive function, memory and language. In the MRI sub-cohort, the frontoparietal networks in the APOE ε4 carrier group exhibited an altered pattern, mainly in the left precentral regions, inferior frontal lobe and angular gyrus. More importantly, the decline of cognitive function was correlated with abnormal FC in the left precentral regions in APOE ε4 carriers. APOE ε4 aggravated the dysfunction in frontal and parietal regions in hypertensive patients. This highlights the importance of brain protection in hypertensive patients, especially those with a genetic risk of AD.