We investigate the delayed feedback control to suppress the vibration in a torsional vibrating system. The delayed feedback control is applied to a torsional vibrating system with a nonlinear dynamical absorber.We investigate the effects of gain and delay on vibration suppression of the primary system. The results show that for a fixed gain, the vibration of the primary system can be suppressed at some values of the delay. As the delay varies for a fixed gain, the amplitude of the primary system can be suppressed to a minimum value. The vibration of the primary system is suppressed form 0.24 to 0.03 when the gain and the delay are chosen to be appropriate values. The analytical solutions are consistent well with the numerical simulation.