A novel dynamic vibration absorber (DVA) with grounded stiffness element and amplifying mechanism is presented, and the optimal parameters are studied in detail. At first, the dynamical equation is established and the analytical solution is obtained. It is found that there are three fixed points independent of damping ratio in the amplitude-frequency curves of the primary system. The optimum frequency ratio of the DVA is obtained based on the fixed-point theory presented by Den Hartog. The optimum grounded stiffness ratio is deduced, and it is found that with the change of the mass ratio and magnification ratio of the amplifying mechanism, there are three cases for the optimum grounded stiffness ratio, i.e., negative, zero and positive. Then, the approximate optimum damping ratio is derived through minimizing the maximum amplitude of the response of the primary system. The DVA with positive grounded stiffness theoretically has the best control performance. Compared with some existing DVAs under the harmonic and random excitations, it could be concluded that the model with optimal parameters in this paper can greatly reduce the resonance amplitude and broaden the frequency band of vibration reduction.