Grazing bifurcation might bring dramatic and abrupt qualitative changes of system responses in non-smooth systems.It is necessary to control the stability of near-grazing dynamics for guaranteeing the persistence of local attractor near grazing orbit.In this paper, the control problem of near-grazing dynamics in a two-degree-of-freedom vibratory system with a clearance is addressed.The discontinuity mapping is built to derive a normal form map near the grazing point.