Rubinstein-Taybi syndrome (RTS) is characterized by peculiar facies, mental retardation, broad thumbs, and great toes. Approximately one-third of the affected individuals have a variety of congenital heart diseases. They can also have upper airway obstruction during sleep, due to hypotonia and the anatomy of the oropharynx and airway, which make these patients susceptible to obstructive sleep apnea (OSA). In our case, pulmonary hypertension was caused, successively, by congenital heart defects (a large patent ductus arteriosus and arch hypoplasia) and obstructive sleep apnea during early infancy. The congenital heart defects were surgically corrected, but persistent pulmonary hypertension was identified 2 months after the operation. This pulmonary hypertension was due to OSA, and it was relieved by nasal continuous positive airway pressure. This case is the first report of pulmonary hypertension from OSA in a young infant with RTS.