We report that preexisting individual differences in the cortical thickness of brain areas involved in a perceptual learning task predict the subsequent perceptual learning rate. Participants trained in a motion-discrimination task involving visual search for a “V”-shaped target motion trajectory among inverted “V”-shaped distractor trajectories. Motion-sensitive area MT+ (V5) was functionally identified as critical to the task: after 3 weeks of training, activity increased in MT+ during task performance, as measured by functional magnetic resonance imaging. We computed the cortical thickness of MT+ from anatomical magnetic resonance imaging volumes collected before training started, and found that it significantly predicted subsequent perceptual learning rates in the visual search task. Participants with thicker neocortex in MT+ before training learned faster than those with thinner neocortex in that area. A similar association between cortical thickness and training success was also found in posterior parietal cortex (PPC).