Taking a new type of the grounded threeelement type dynamic vibration absorber as the research object, the optimal analytical solution is studied based on H∞ optimization principle in this paper. Firstly, a series viscoelastic model is introduced into the grounded dynamic vibration absorber, and the analytical solution of the system is obtained based on the established motion differential equation. Three fixed points are found in the amplitudefrequency curves of the primary system. Moreover, the design formulae for the optimal tuning ratio and the optimal stiffness ratio of the dynamic vibration absorber are developed by adjusting the three fixed points to the same height according to the fixed point theory. Then, the optimal damping ratio is obtained by minimizing the maximum value of the amplitudefrequency curves according to H∞ optimization principle. In addition, the comparison between the numerical solution and the analytical solution is investigated. It verifies the correctness of the analytical solution, and illustrates that the grounded threeelement type dynamic vibration absorber exhibites better performance of vibration absorption.