Considering the nonlinear characteristic of tire’s grounding friction, a polygonal wear model of tire was established based on variable stiffness of lateral. Then the stability of system was analyzed，and the self-excited vibration of tire was proved to be a kind of stable periodic vibration caused by Hopf bifurcation of system. Finally, the ranges of speed and toe-in angle which could motivate self-excited vibration were given through numerical simulation. The results showed that the polygonal wear was a typical nonlinear self-excitation vibration phenomenon caused by the tread’s lateral self-excited vibration, and the polygonal number was equivalent to the ratio of the lateral vibration frequency of tire tread to the rotational frequency of tire. This model could explain the formation mechanism of the polygonal wear of tire.