The Poincaré map of periodic motion was established, and the bifurcation diagram of two parameters was obtained by using an explicit critical criterion without using eigen values when the difficulties caused by the classical Neimark-Sacker bifurcation critical criterion described by the properties of eigenvalues were considered. The bifurcation diagram helps to proactively design the quasi-periodic impact motion of the system. Then, the stability of the quasi-periodic impact motion was further analyzed by utilizing the center manifold and normal formal theory. Finally, numerical experiments verify that the stable quasi-periodic impact motion can be generated at chosen parameters points.