There has been an increasing demand for the design of an optimum topological layout in several engineering fields for a simple part, along with a system that considers the relative behaviors between adjacent parts. This paper presents a method of designing an optimum topological layout to achieve a linear dynamic impact and frictionless contact conditions in which relative behaviors can be observed between adjacent deformable parts. The solid isotropic method with penalization (SIMP) method is used with an appropriate filtering scheme to obtain an optimum topological layout. The condensed mortar method is used to handle the non-matching interface, which inevitably occurs in the impact and contact regions, since it can easily apply the existing well-known topology optimization approach even in the presence of a non-matching interface. The validity of the proposed method is verified through a numerical example. In the future, the proposed optimization approach will be applied to more general and highly nonlinear non-matching interface problems, such as friction contact and multi-physics problems.