Based on the special dynamical property of continuous transition at certain degenerate grazing points in the single-degree-of-freedom impact oscillator, the control problem of the grazing-induced chaos is investigated in this paper. To design degenerate grazing bifurcations, we show how to obtain the degenerate grazing points of the 1/n impact periodic motions by the existence and stability analysis first. Then, a discrete-in-time feedback control strategy is used to suppress the grazing-induced chaos into the 1/n impact periodic motions precisely by the desired degenerate grazing bifurcation. The feasibility of the control strategy is verified by numerical simulations.