Various cognitive differences have been reported between consistent and weak handers (Prichard, Propper, & Christman, 2013), but little is known about the neurobiological factors that may be associated with this distinction. The current study examined cortical structural lateralization and corpus callosum volume in a large, well-matched sample of young adults (N = 164) to explore potential neurostructural bases for this hand group difference. The groups did not differ in corpus callosum volume. However, at the global hemispheric level, weak handers had reduced or absent asymmetries for gray and white matter volume, cortical surface area, thickness, and local gyrification, relative to consistent handers. Group differences were also observed for some regional hemispheric asymmetries, the most prominent of which was reduced or absent gyrification asymmetry for weak handers in a large region surrounding the central sulcus and extending into parietal association cortex. The findings imply that variations in handedness strength are associated with differences in structural lateralization, not only in somatomotor regions, but also in areas associated with high level cognitive control of action.