This paper describes the analysis of a dynamic vibration absorber with absolute damping which acts on the absorber mass alone. The analysis shows that the effectiveness of the dynamic absorber with absolute damping is greater than that of the conventional dynamic absorber. Two conditions of the main mass system are considered for the optimum tuning: the main mass system has undamping or damping. In the undamped system, the optimum tuning and damping of the dynamic absorber are formulated on the basis of the theory of fixed points. In the damped system, the optimum values of the dynamic absorber are obtained through the numerical analysis to minimize the two resonant amplitudes. The numerical results are given by the convenient empirical formulae. Also it is explained that the dynamic absorber has the effect of vibration prevention in the characteristic with a single resonance.