BACKGROUND: It is known that eyes-open (EO) and eyes-closed (EC) conditions invoke different organizations of brain functional networks, such as sensorimotor, attention, and salience networks in healthy participants. Functional connectivity (FC) extracted from resting-state functional magnetic resonance imaging data, under either EO or EC conditions, has been widely applied to explore the neural substrates of Alzheimer's disease (AD). However, the impact of eye conditions on FC within the AD continuum remains not fully understood. OBJECTIVE: This study aims to investigate the effects of eye conditions on FC across the AD continuum. METHODS: FC with the primary visual cortex (V1) seed was analyzed for both EO and EC conditions in 59 amyloid-β (Aβ)-positron emission tomography (PET)-negative cognitively normal (CN-), 14 Aβ-PET-positive CN+, 24 mild cognitive impairment (MCI+), and 15 AD individuals. RESULTS: EO and EC differently modulated FC between the V1 and cerebellum, especially the posterior vermis, in all groups. In CN-, CN+, and MCI+ groups, EO significantly facilitated FC between V1 and the cerebellum compared with the EC condition. However, the AD group showed the reverse pattern. Moreover, a sub-analysis demonstrated that the FC significantly correlated with a truncal balance measure under EO, but not EC, in participants with MCI+ and AD. CONCLUSIONS: The results show that the FC between the V1 and cerebellum changed in AD. This finding may partially explain the impaired truncal balance and tendency to fall down in AD. This study suggests that analyzing FC under EO and EC conditions may provide a new functional biomarker for AD.