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Previous studies have shown that a higher intensity of physical activity (PA) is associated with a lower risk of cognitive impairment (CI), whereas hypertension is associated with higher CI. However, there are few studies on the association between PA intensity and cognitive function in hypertensive patients. This study investigated the association between PA intensity and cognitive function in hypertensive patients. A total of 2035 hypertensive patients were included in this study, including 407 hypertensive patients with CI and 1628 hypertensive patients with normal cognitive function matched 1:4 by age and sex. The International Physical Activity Questionnaire-Long Form and the Mini-mental State Examination were used to evaluate PA intensity, total metabolic equivalents, and cognitive function in patients with hypertension. Multivariate logistic regression was used to analyze the correlation between PA intensity and CI in hypertensive patients. The Spearman correlation coefficient was used to analyze the correlation between PA intensity and the total score of each component of the MMSE and the correlation between PA total metabolic equivalents and cardiac structure in hypertensive patients. After adjusting for all confounding factors, PA intensity was negatively associated with CI in hypertensive patients (OR = 0.608, 95% CI: 0.447–0.776, P < 0.001), and this association was also observed in hypertensive patients with education level of primary school and below and junior high school and above (OR = 0.732, 95% CI: 0.539–0.995, P = 0.047; OR = 0.412, 95% CI: 0.272–0.626, P < 0.001). The intensity of PA in hypertensive patients was positively correlated with orientation (r = 0.125, P < 0.001), memory (r = 0.052, P = 0.020), attention and numeracy (r = 0.151, P < 0.001), recall ability (r = 0.110, P < 0.001), and language ability (r = 0.144, P < 0.001). PA total metabolic equivalents in hypertensive patients were negatively correlated with RVEDD and LAD (r = − 0.048, P = 0.030; r = − 0.051, P = 0.020) and uncorrelated with LVEDD (r = 0.026, P = 0.233). Higher PA intensity reduced the incidence of CI in hypertensive patients. Therefore, hypertensive patients were advised to moderate their PA according to their circumstances. [ABSTRACT FROM AUTHOR]