Childhood obstructive sleep apnea (OSA) is a sleeping disorder commonly affecting school-aged children and is characterized by repeated episodes of blockage of the upper airway during sleep. In this study, we performed a graph theoretical analysis on the brain morphometric correlation network in 25 OSA patients (OSA group; 5 female; mean age, 10.1 ± 1.8 years) and investigated the topological alterations in global and regional properties compared with 20 healthy control individuals (CON group; 6 females; mean age, 10.4 ± 1.8 years). A structural correlation network based on regional gray matter volume was constructed respectively for each group. Our results revealed a significantly decreased mean local efficiency in the OSA group over the density range of 0.32-0.44 (p < 0.05). Regionally, the OSAs showed a tendency of decreased betweenness centrality in the left angular gyrus, and a tendency of decreased degree in the right lingual and inferior frontal (orbital part) gyrus (p < 0.005, uncorrected). We also found that the network hubs in OSA and controls were distributed differently. To the best of our knowledge, this is the first study that characterizes the brain structure network in OSA patients and invests the alteration of topological properties of gray matter volume structural network. This study may help to provide new evidence for understanding the neuropathophysiology of OSA from a topological perspective.