A viability criterion of a polytopic set for a linear control system is discussed by using nonsmooth analysis. It is shown that, determining the viability of a polytopic set, which is expressed by a convex hull of a finitely many points, can be transformed into verifying the viability criteria at vertices without the assumption that the input set is an polytope, which is needed in existing criteria. This method of determining the viability is easy to be complemented. Finally, the viable design is discussed by using the proposed viability criterion.