The objectives are to explore the demographic and polysomnographic features of children with Down syndrome and to determine the predictive factors associated with severe sleep apnea. A total of 81 children with Down syndrome referred for full-night polysomnography were analyzed. In addition, parental interviews were performed for each child. Data were available for 81 children, with a mean age of 4.8 years. Severe obstructive sleep apnea was determined in 53.1%. Age, sex, exposure to second-hand smoke, clinical findings, anthropometric features, and the presence of comorbidities were not predictors of severe obstructive sleep apnea. Children who were exposed to second-hand smoke had more sleep-related symptoms. Even in children without symptoms, the prevalence of severe obstructive sleep apnea was 40%. Moreover, 86% of parents had no previous information regarding possible sleep breathing disorders in their children. Clinically significant central apnea was present in 10 patients (12.3%). Conclusion: Our results demonstrate that severe obstructive sleep apnea is common in children with Down syndrome, even in children without a history of symptoms of sleep apnea. It is not possible to predict patients with severe apnea; thus, screening of children with Down syndrome beginning from young ages is very important. Central apneas could be a part of the spectrum of sleep abnormalities in Down syndrome.