The problem of viability for a class of nonlinear uncertain systems is studied. A sufficient and necessary condition of viability for the convex compact set under this system via support functions is presented. When the viable set is a polytope, sufficient conditions for the sum form and intersection form of the polytope are given to determine the viability. Finally, a numerical example is presented to illustrate the result, and the example shows that the main result also gives a condition of viability for a kind of switched systems.