Shape complementarity is an important component of molecular recognition, and the ability to precisely adjust the shape of a binding scaffold to match a target of interest would greatly facilitate the creation of high-affinity protein reagents and therapeutics. Here we describe a general approach to control the shape of the binding surface on repeat-protein scaffolds and apply it to leucine-rich-repeat proteins. First, self-compatible building-block modules are designed that, when polymerized, generate surfaces with unique but constant curvatures. Second, a set of junction modules that connect the different building blocks are designed. Finally, new proteins with custom-designed shapes are generated by appropriately combining building-block and junction modules. Crystal structures of the designs illustrate the power of the approach in controlling repeat-protein curvature.