Human skill learning requires fine-scale coordination of distributed networks of brain regions linked by white matter tracts to allow for effective information transmission. Yet how individual differences in these anatomical pathways may impact individual differences in learning remains far from understood. Here, we test the hypothesis that individual differences in structural organization of networks supporting task performance predict individual differences in the rate at which humans learn a visuomotor skill. Over the course of 6 weeks, 20 healthy adult subjects practiced a discrete sequence production task, learning a sequence of finger movements based on discrete visual cues. We collected structural imaging data, and using deterministic tractography generated structural networks for each participant to identify streamlines connecting cortical and subcortical brain regions. We observed that increased white matter connectivity linking early visual regions was associated with a faster learning rate. Moreover, the strength of multiedge paths between motor and visual modules was also correlated with learning rate, supporting the potential role of extended sets of polysynaptic connections in successful skill acquisition. Our results demonstrate that estimates of anatomical connectivity from white matter microstructure can be used to predict future individual differences in the capacity to learn a new motor–visual skill, and that these predictions are supported both by direct connectivity in visual cortex and indirect connectivity between visual cortex and motor cortex.