The development of cerebral white matter involves both myelination and pruning of axons, and the balance between these two processes may differ between individuals. Cross-sectional measures of white matter development mask the interplay between these active developmental processes and their connection to cognitive development. We followed a cohort of 39 children longitudinally for three years, and measured white matter development and reading development using diffusion tensor imaging and behavioral tests. In the left arcuate and inferior longitudinal fasciculus, children with above-average reading skills initially had low fractional anisotropy (FA) with a steady increase over the 3-year period, while children with below-average reading skills had higher initial FA that declined over time. We describe a dual-process model of white matter development that balances biological processes that have opposing effects on FA, such as axonal myelination and pruning, to explain the pattern of results.