A balanced excitation-inhibition ratio (E/I ratio) is critical for healthy brain function. Normative development of cortex-wide E/I ratio remains unknown. Here we non-invasively estimate a putative marker of whole-cortex E/I ratio by fitting a large-scale biophysically-plausible circuit model to resting-state functional MRI (fMRI) data. We first confirm that our model generates realistic brain dynamics in the Human Connectome Project. Next, we show that the estimated E/I ratio marker is sensitive to the GABA-agonist benzodiazepine alprazolam during fMRI. Alprazolam-induced E/I changes are spatially consistent with positron emission tomography measurement of benzodiazepine receptor density. We then investigate the relationship between the E/I ratio marker and neurodevelopment. We find that the E/I ratio marker declines heterogeneously across the cerebral cortex during youth, with the greatest reduction occurring in sensorimotor systems relative to association systems. Importantly, among children with the same chronological age, a lower E/I ratio marker (especially in association cortex) is linked to better cognitive performance. This result is replicated across North American (8.2 to 23.0 years old) and Asian (7.2 to 7.9 years old) cohorts, suggesting that a more mature E/I ratio indexes improved cognition during normative development. Overall, our findings open the door to studying how disrupted E/I trajectories may lead to cognitive dysfunction in psychopathology that emerges during youth.