Background: Fear of falling (FoF) in the elderly is one of the major public health concerns in this era of aging of the population. As there is limited evidence on how cognitive function may differ by social support level in relation to FoF among the elderly, this cross-sectional study aims to investigate the prevalence of FoF and the associations between cognitive impairment and FoF by the social support level, after adjustments for potential confounders. Methods: Data from the "Health needs assessment of elderly in Thua Thien Hue Province, Vietnam in 2018" survey of 725 elderly aged 60 years or older were used for analysis. FoF was assessed using the Fall Efficacy Scale-International. High FoF was defined as a score above 28. The Multidimensional Scale of Perceived Social Support was used to measure the perception of support. Logistic regression analysis was performed to investigate the association between cognitive function and FoF by social support levels (p < 0.05). Results: The prevalence of high FoF among the elderly was 40.8%. Female gender, advanced age, a marital status of single or formerly married, living alone, history of injury, history of falls, chronic diseases (arthritis and/or hypertension), limitations of the IADL and BADL, visual difficulty and walking difficulty, low social support, and cognitive impairment were all significantly associated with a high FoF. After adjustments for the age, gender, marital status, history of falls and health-related factors, cognitive impairment remained significantly associated with a high FoF among the elderly with a low to moderate social support level (OR = 2.97, 95% CI 1.49-5.89), but not in those with a high social support level. Conclusions: A high FoF was associated with impairment of cognitive function among the elderly who perceived themselves as having low or moderate support levels, even after adjustments for socio demographic and physical functional factors. However, this association was not observed among the elderly who perceived themselves as having high social support levels. Fall prevention programs for the elderly with various levels of social support should be carefully devised, keeping in mind the cognitive function levels of the target recipients.