Individual differences in cognition during childhood are associated with important social, physical, and mental health outcomes in adolescence and adulthood. Given that cortical surface arealization during development reflects the brain’s functional prioritization, quantifying variation in the topography of functional brain networks across the developing cortex may provide insight regarding individual differences in cognition. We test this idea by defining personalized functional networks (PFNs) that account for interindividual heterogeneity in functional brain network topography in 9-10 year olds from the Adolescent Brain Cognitive Development^SM Study. Across matched discovery (n=3,525) and replication (n=3,447) samples, the total cortical representation of fronto-parietal PFNs positively correlated with general cognition. Cross-validated ridge regressions trained on PFN topography predicted cognition across domains, with prediction accuracy increasing along the cortex’s sensorimotor-association organizational axis. These results establish that functional network topography heterogeneity is associated with individual differences in cognition before the critical transition into adolescence.