Both the Legendre transformation between Lagrange′s equations and Hamilton′s equations and the canonical transformation theory of Hamilton′s equations play an important role in analytical mechanics. There seems to be no relationship between them from a local perspective. In this paper, based on the Lagrangian submanifold theory of symplectic manifold, the unified geometric interpretation of the canonical transformation theory and the Legendre transformation theory was given globally. Then, by utilizing geometric mechanics, the geometric structure of the canonical transformation for a Hamilton system and the geometric Legendre transformation between Lagrange′s equations and Hamilton′s equations were clearly described.