Background Intensively treating hypertension may benefit cardiovascular disease and cognitive function, but at the short-term expense of reduced kidney function. Methods We investigated markers of kidney function and the effect of intensive hypertension treatment on incidence of dementia and mild cognitive impairment (MCI) in 9361 participants in the randomized Systolic Blood Pressure Intervention Trial, which compared intensive versus standard systolic BP lowering (targeting,120 mm Hg versus,140 mm Hg, respectively). We categorized participants according to baseline and longitudinal changes in eGFR and urinary albumin-to-creatinine ratio. Primary outcomes were occurrence of adjudicated probable dementia and MCI. Results Among 8563 participants who completed at least one cognitive assessment during follow-up (median 5.1 years), probable dementia occurred in 325 (3.8%) and MCI in 640 (7.6%) participants. In multivariable adjusted analyses, there was no significant association between baseline eGFR,60 ml/min per 1.73 m2 and risk for dementia or MCI. In time-varying analyses, eGFR decline $30% was associated with a higher risk for probable dementia. Incident eGFR,60 ml/min per 1.73 m2 was associated with a higher risk for MCI and a composite of dementia or MCI. Although these kidney events occurred more frequently in the intensive treatment group, there was no evidence that they modified or attenuated the effect of intensive treatment on dementia and MCI incidence. Baseline and incident urinary ACR $30 mg/g were not associated with probable dementia or MCI, nor did the urinary ACR modify the effect of intensive treatment on cognitive outcomes. Conclusions Among hypertensive adults, declining kidney function measured by eGFR is associated with increased risk for probable dementia and MCI, independent of the intensity of hypertension treatment.