What is the neural code for object shape? Despite intensive research, the precise nature of object representations in high-level visual cortex remains elusive. Here we use functional magnetic resonance imaging (fMRI) to show that convex shapes are encoded in a privileged fashion by human lateral occipital complex (LOC), a region which has been implicated in object recognition. On each trial, two convex or two concave shapes that were either identical or different were presented sequentially. Critically, the convex and concave stimuli were the same except for a binocular disparity change that reversed the figure-ground assignment. The fMRI response in LOC for convex stimuli was higher for different than for identical shape pairs, indicating sensitivity to differences in convex shape. However, when the same stimuli were seen as concave, the response for different and identical pairs was the same, indicating lower sensitivity to changes in concave shape than convex shape. This pattern was more pronounced in the anterior than in the posterior portion of LOC. These results suggest that convex contours could be basic building blocks of cortical object representations.