Hypertension is associated with cognitive deficits, probably caused by cerebral small vessel disease. The authors examined whether additional presence of cardiac and renal organ damages, and their combined presence, are associated with future cognitive performance. In 78 patients with essential hypertension (mean age 51.2 ± 12.0 years), brain damage was determined by MRI features, cardiac damage by left ventricular mass index (LVMI), and renal damage by estimated glomerular filtration rate (eGFR) and albuminuria. At 9‐year follow‐up, neuropsychological assessment was performed. LVMI was associated with future lower cognition (P = 0.032), independent of age, sex, premorbid cognition, and brain damage, but eGFR and albuminuria were not. The presence of 2 or 3 types of organ damage compared to none was associated with future lower cognition. Increasing number of hypertensive organ damages, and cardiac damage independently of brain damage, might indicate a more severe hypertensive disease burden and could help to identify patients at risk of cognitive problems.