In order to obtain more conservative results in the analysis of the stability of the time-delayed torsional vibration system, the integral inequality method is used to study the stability of the system, and the derived theorem is used to analyze the stability of the system inhibited by the neutral time-delayed dynamic vibration absorber. The results show that the conservative upper bound of time delay under different parameters can be obtained by using this theorem. The numerical simulation also confirms the correctness of the analytical results and provides guidance for the designers of the systems using neutral time-delay dynamic vibration absorber to suppress linear forced torsional vibration.