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This paper deals with the active vibration control of the drill-string torsional dynamics. The drill-string is modelled considering only torsional vibrations. The system is discretized by means of the finite element model and reduced using the normal modes of the associate homogeneous conservative system. An external controlled torque is applied at the top of the drill-string. The nonlinear interaction between the rock and the bit is included in the model, and it is a function of the bit rotation, friction, rock properties and axial load. The control strategy employed is the PD-control strategy and a state space controller. The torsional stability for different weight-on-bit values and top speeds are analyzed. It is shown that the control strategy applied increases the stability region of the system.