Abstract: A mathematical model of a four-degree-of-freedom vibro-impact system is established,deriving the eight-dimensional Poincar?maps of periodic motion in the system,calculating the centre manifold and showing the steps for the reduction of high-dimensional maps to a two-dimensional one. The stability of periodic motion is studied,the Hopf bifurcation and period-doubling bifurcation phenomena of periodic motion in the system are analyzed based on the suitable parameter combination,and the existence of the Hopf bifurcation is verified in a four-degree-of-freedom vibro-impact system. The evolution process of the system to chaos and the system invariant torus are simulated numerically. Consequently,the formation process of instability and chaos of invariant torus in the vibro-impact system are revealed.