A non-traditional dynamic vibration absorber is proposed for the minimization of maximum vibration velocity response of a vibrating structure. Unlike the traditional damped absorber configuration, the proposed absorber has a linear viscous damper connecting the absorber mass directly to the ground instead of the main mass. Optimum parameters of the proposed absorber are derived based on the fixed-point theory for minimizing the maximum vibration velocity response of a single-degree-of-freedom system under harmonic excitation. The extent of reduction in maximum vibration velocity response of the primary system when using the traditional dynamic absorber is compared with that using the proposed one. Under the optimum tuning condition of the absorbers, it is proved analytically that the proposed absorber provides a greater reduction in maximum vibration velocity response of the primary system than the traditional absorber.