In order to study the relation of the period-doubling bifurcation and the Hopf bifurcation,the period-doubling bifurcation problems of a vibro-impact system is investigated when the periodical solutions lose its stability. First, the process of establishing the Poincaré map of the 1-1 motion of this system is provided. Second, the probability of the period-doubling bifurcation is analysed according to the Eigenvalue cross the unit circle. Finally, numerical simulation results demonstrate it. The typical period-doubling bifurcation is found. After the Hopf bifurcation in a non-resonance case, the non typical period doubling bifurcations occur while one single parameter varies crossing the resonance neighborhood. The number of orbits of the period doubling bifurcation cascade depends on the order of strong (weak) resonance.
