The robust stability for a class of timedelay system with delay dependent parameters was discussed.On the basis of “geometric stability switches criteria”, a new stabilization criterion “stability switches point method” was established.Using the new criterion, the region of the parameters which make the equilibrium asymptotically stable can be obtained easily.As an application, the sunflower equation was studied, and the result shows that one can obtain not only the stable region but also the Hopf bifurcation points with the help of mathematic software: Maple.Moreover, the robust stability of the equilibrium can be reached by adjusting the time delay to proper values.