Children vary greatly in their vocabulary development during preschool years. Importantly, the pace of this early vocabulary growth predicts vocabulary size at school entrance. Despite its importance for later academic success, not much is known about the relation between individual differences in early vocabulary development and later brain structure and function. Here we examined the association between vocabulary growth in children, as estimated from longitudinal measurements from 14 to 58 months, and individual differences in brain structure measured in 3rd and 4th grade (8–10 years old). Our results show that the pace of vocabulary growth uniquely predicts cortical thickness in the left supramarginal gyrus. Probabilistic tractography revealed that this region is directly connected to the inferior frontal gyrus (pars opercularis) and the ventral premotor cortex, via what is most probably the superior longitudinal fasciculus III. Our findings demonstrate, for the first time, the relation between the pace of vocabulary learning in children and a specific change in the structure of the cerebral cortex, specifically, cortical thickness in the left supramarginal gyrus. They also highlight the fact that differences in the pace of vocabulary growth are associated with the dorsal language stream, which is thought to support speech perception and articulation.