Hypertension is a risk factor for diffuse brain atrophy. Yet, there is little evidence that higher blood pressure predicts focal brain atrophy, as indicated by a lower volume of regional brain tissue. This voxel-based morphometry study tested (a) whether higher blood pressure predicts lower regional grey or white matter volume and (b) whether a blood-pressure-related reduction in regional brain tissue volume predicts poorer neuropsychological test performance. Participants were 76 men (M age = 61.33, SD = 4.95 years) and 58 women (M age = 59.86, SD = 5.10 years) without a cardiovascular, cerebrovascular, or neuropsychiatric disease. Results showed that among men, higher resting systolic blood pressure predicted lower grey matter volume in the supplementary motor area and adjacent superior frontal gyrus, the anterior cingulate cortex, and middle temporal gyrus. Among men, lower grey matter volume in the supplementary motor area also predicted a slower time to complete the Trail Making Part B Test of executive control and a poorer recall of items from the Four-word Short-term Memory Test of working memory. These relationships were independent of age, total brain tissue volume, educational history, severity of carotid atherosclerosis, and the extent of periventricular and subcortical white matter lesions. Among women, no statistically significant relationships were found between blood pressure, regional brain tissue volume, and cognitive function. These findings suggest a functional relationship among men between higher blood pressure, lower regional grey matter volume, and poorer cognitive function that is independent of other risk factors and confounding medical conditions.