Sleep-disordered breathing (SDB), characterized by abnormal respiratory patterns or inadequate quantity of ventilation, is common in adults. A positive association between SDB and hypertension has been established, in both cross-sectional and longitudinal studies. One void in the literature concerns the role of race/ethnicity in the association between SDB and hypertension. In this context, a cross-sectional study was performed on 6,783 participants in the National Health and Nutrition Examination Survey 2005–2008. Participants were ≥age 20 and free from cardiovascular disease. The outcome of interest was hypertension, defined as ≥140 mmHg systolic blood pressure (BP), and/or ≥90 mmHg diastolic BP or antihypertensive medication use. Self-reported SDB was positively associated with hypertension, independent of confounders such as depression, diabetes, cholesterol levels, and body mass index, among others. The association persisted in subgroup analyses by gender, with a stronger association among males than females, as well as by race/ethnicity, with non-Hispanic blacks displaying the strongest association. In the multivariable-adjusted model, compared to a sleep summary score of zero (referent), the OR (95% CI) of hypertension for non-Hispanic blacks was 1.34 (0.98–1.83) for a sleep summary score of 1, 1.44 (1.06–1.97) for a score of 2 and 3.72 (1.98–7.00) for a score of >3; p-trend < 0.0001. SDB was positively associated with hypertension in a large, nationally representative sample of US adults. Along with being prevalent, SDB is also treatable. Therefore, our results are important for minority race/ethnic groups who typically experience a higher baseline for negative health outcomes.