Reduced global motion sensitivity, relative to global static form sensitivity, has been found in children with many neurodevelopmental disorders, leading to the "dorsal stream vulnerability" hypothesis (Braddick et al., 2003). Individual differences in typically developing children's global motion thresholds have been shown to be associated with variations in specific parietal cortical areas (Braddick et al., 2016). Here, in 125 children aged 5-12years, we relate individual differences in global motion and form coherence thresholds to fractional anisotropy (FA) in the superior longitudinal fasciculus (SLF), a major fibre tract communicating between parietal lobe and anterior cortical areas. We find a positive correlation between FA of the right SLF and individual children's sensitivity to global motion coherence, while FA of the left SLF shows a negative correlation. Further analysis of parietal cortical area data shows that this is also asymmetrical, showing a stronger association with global motion sensitivity in the left hemisphere. None of these associations hold for an analogous measure of global form sensitivity. We conclude that a complex pattern of structural asymmetry, including the parietal lobe and the superior longitudinal fasciculus, is specifically linked to the development of sensitivity to global visual motion. This pattern suggests that individual differences in motion sensitivity are primarily linked to parietal brain areas interacting with frontal systems in making decisions on integrated motion signals, rather than in the extra-striate visual areas that perform the initial integration. The basis of motion processing deficits in neurodevelopmental disorders may depend on these same structures.