Background: Frailty is commonly considered as a syndrome with several symptoms, including weight loss, exhaustion, weakness, slow walking speed and physical inactivity. It has been suggested that cognitive impairment should be included in the frailty index, however the association between frailty and cognition has not yet been fully established. Objective: To investigate cross-sectionally whether frailty is associated with cognitive impairment or clinically diagnosed dementia in older people. Methods: The study included a total of 654 persons aged 76-100 years (mean 82 ± 4.6). Frailty status of the participants was assessed using the Cardiovascular Health Study criteria. Cognitive function was assessed with the Mini-Mental State Examination (MMSE). Clinically diagnosed dementia was assessed by specialists using diagnostic criteria. The associations between frailty and cognition were investigated using logistic regression. Results: A total of 93 (14%) participants were classified as frail. Cognitive impairment (MMSE score <25) was observed among 171 (26%) persons and 134 (21%) persons had clinically diagnosed dementia. 97 (15%) persons had Alzheimer's disease, 19 (3%) had vascular dementia, 12 (2%) had dementia with Lewy bodies and 8 persons (1%) had some other type of dementia. Multivariate logistic regression models showed that frail persons were almost 8 times more likely to have cognitive impairment (OR 7.8, 95% CI 4.0-15.0), 8 times more likely to have some kind of dementia (OR 8.0, 95% CI 4.0-15.9), almost 6 times more likely to have vascular dementia (OR 5.6, 95% CI 1.2-25.8) and over 4 times more likely to have Alzheimer's disease (OR 4.5, 95% CI 2.1-9.6) than persons who were robust. Conclusion: Frailty is strongly associated with cognitive impairment and clinically diagnosed dementia among persons aged 76 and older. It is possible that cognitive impairment is a clinical feature of frailty and therefore should be included in the frailty definition.