High blood pressure (BP) in middle-aged and older adults is associated with lower brain volume and cortical thickness assessed with structural MRI. However, little evidence is available in young adults. We investigated the associations of high BP with brain volumes and cortical thickness in healthy young adults. This cross-sectional study included 1095 young adults (54% women, 22-37 years) from the Human Connectome Project (HCP) who self-reported not having a history of hypertension or taking antihypertensive medications. Brachial systolic (SBP) and diastolic BP (DBP) were measured with semi-automatic or manual sphygmomanometer during study visits. Structural MRI was used to measure gray matter (GM) and white matter (WM) volume and mean cortical thickness. Associations of BP and hypertension stage with total and regional brain volumes and cortical thickness were analyzed using linear regression and analysis of covariance (ANCOVA) after adjusting for age, sex, education years, body mass index (BMI), smoking, alcohol consumption history, zygosity, and total intracranial volume. SBP and DBP were (mean ± SD) 123.6 ± 14.2 and 76.5 ± 10.6 mmHg, respectively (n = 1095). High DBP was associated with lower total GM (p = 0.012), cortical GM (p = 0.004), subcortical GM (p = 0.012), and total WM volumes (p = 0.031). High SBP and DBP were associated with lower regional cortical volume and cortical thickness. These findings suggest that high BP may have deleterious effects on brain health at the early stage of adulthood.