Children born very preterm are at significant risk of neurodevelopmental impairment. This study sought to identify differences in cognitive function in children born very preterm compared to term-born controls and investigate alteration in white matter microstructure and functional connectivity (FC) based on tract-based spatial statistics (TBSS) and resting-state functional MRI, respectively. At 6 years of age, 36 children born very preterm (< 32 weeks' gestation) without major neurological disabilities and 26 term-born controls were tested using the Wechsler Intelligence Scale for Children, 4th edition, and Child Behavior Checklist. Whole-brain deterministic tractography and FC measurements were performed in both groups. The very preterm group had significantly lower intelligence scores than the term-born controls. The TBSS revealed no significant differences between the two groups, whereas FC was significantly increased between the frontoparietal network and the language network and was significantly decreased between the right salience network nodes in the very preterm group. The altered FC patterns between specific regions of the higher-order networks may reflect underlying deficits in the functional network architecture associated with cognitive function. Further studies are needed to demonstrate a direct connection between FC in these regions and cognitive function.