In this paper， the effect of top drive control on stick-slip and bit-bounce was studied numerically based on a three-degreeof-freedom lumped parameter model considering coupling between axial and torsional vibrations of drill strings. The simulation re? sults indicate that although the tuned k-c control can inhibit the stick-slip and bit-bounce the drill string vibration system to a certain extent， the suppression effect of stick-slip and bit-bounce in the drill string vibration system is not ideal when the input angular ve? locity is high and the nominal drilling pressure is low， or the input angular velocity is small and the nominal drilling pressure is large. The tuned I-k-c control can successfully eliminate the influence of input angular velocity and nominal drilling pressure chang? es on stick-slip and bit-bounce， so that no matter what the input angular velocity and nominal drilling pressure values are， the bit speed will remain stable around the given input angular velocity， reducing the fluctuation of WOB， TOB and axial displacement. Therefore， compared to top-drive tuned k-c control， tuned I-k-c control is more efficient in suppressing the stick-slip and bitbounce of drill string vibration system.