Aim: This study aimed to examine the cross-sectional association between cognitive function and elder abuse. Methods: The Chicago Health and Aging Project (CHAP) is a population-based study conducted in a geographically defined community (n = 8,932). We identified 238 CHAP participants who had elder abuse reported to a social services agency. Cognitive function was assessed using the Mini-Mental State Examination (MMSE), the Symbol Digit Modalities Test (perceptual speed), and both immediate and delayed recall of the East Boston Memory Test (episodic memory). An index of global cognitive function scores was derived by averaging the z-scores of all tests. Logistic regression models were used to assess the association of cognitive function domains and risk of elder abuse. Results: After adjusting for confounders, lowest tertiles of global cognition (odd’s ratio, OR 4.18, 95% confidence interval, 95% CI 2.44–7.15), MMSE (OR 2.97, 95% CI 1.93–4.57), episodic memory (OR 2.27, 95% CI 1.49–3.43) and perceptual speed (OR 2.37, 95% CI 1.51–3.73) were associated with increased risk of elder abuse. The lowest levels of global cognitive function were associated with an increased risk of physical abuse (OR 3.56, 95% CI 1.08–11.67), emotional abuse (OR 3.02, 95% CI 1.41–6.44), caregiver neglect (OR 6.24, 95% CI 2.68–14.54), and financial exploitation (OR 3.71, 95% CI 1.88–7.32). Conclusion: Lower levels of global cognitive function, MMSE, episodic memory and perceptual speed are associated with an increased risk of elder abuse.