The organization of lipids in biological membranes is essential for cellular functions such as signal transduction and membrane trafficking. A major challenge is how to control lateral lipid composition in supported membranes, which is crucial for the design of biosensors and investigation of cellular processes involved with biomembranes. Here, we undertake the first theoretical study of the full phase behavior of lateral organization of lipids in mixed bilayers induced by a periodically corrugated substrate. A rich variety of compositional segregation of lipids is regulated by varying the roughness of substrates. Interestingly, several structures of our work are similar to the results of the recent experiments with ternary lipid bilayers supported on corrugated substrates, and two novel structures which have not been experimentally observed are also predicted. The morphology diagram, which provides a useful guidance for the future experiments to find unexpected structures, is given. Further, we analyze the microscopic mechanism of the structural formation and demonstrate that our conclusions also remain valid for the case of the substrate with arbitrarily distributed grooves.