Increasing evidence indicates that multiple structures in the brain are associated with intelligence and cognitive function at the network level. The association between the grey matter (GM) structural network and intelligence and cognition is not well understood. We applied a multivariate approach to identify the pattern of GM and link the structural network to intelligence and cognitive functions. Structural magnetic resonance imaging was acquired from 92 healthy individuals. Source-based morphometry analysis was applied to the imaging data to extract GM structural covariance. We assessed the intelligence, verbal fluency, processing speed, and executive functioning of the participants and further investigated the correlations of the GM structural networks with intelligence and cognitive functions. Six GM structural networks were identified. The cerebello-parietal component and the frontal component were significantly associated with intelligence. The parietal and frontal regions were each distinctively associated with intelligence by maintaining structural networks with the cerebellum and the temporal region, respectively. The cerebellar component was associated with visuomotor ability. Our results support the parieto-frontal integration theory of intelligence by demonstrating how each core region for intelligence works in concert with other regions. In addition, we revealed how the cerebellum is associated with intelligence and cognitive functions.