The vibration suppression of torsional vibrating system is investigated by using the delayed vibration absorber. The stability switch method was applied to analyze the stability of the delayed vibration absorber and the combined system, and their stable and unstable regions were obtained respectively. The results show that the vibration of the primary system could be suppressed absolutely when the delay is chosen as the critical stable value of the delayed vibration absorber. The vibration of the primary system could be suppressed partly when the delay is chosen in the stable region of the delayed vibration absorber. As the value of the delay increases, the vibration suppression ability is improved. If the value of the delay is larger than the critical value of the combined system, the structure of the combined system could be destroyed. The analytical results agree with the numerical simulation well.