Because the underlying physiology of pathological tremor in a Parkinson's patient is not well understood, the existing physical and drug therapies have not been successful in tremor treatment. Different mathematical modeling of such vibration has been introduced to investigate the problem and reduce the existing vibration. Most of the models have represented the induced vibration as a sinusoidal wave for mathematical simplification. In this study, a more realistic model based on random vibration was used to attack the problem of tremor suppression. A simple approach for suppressing the tremor associated with Parkinson's disease was presented. This paper was concerned with a multi-objective approach for optimum design of linear vibration absorber subject to random vibrations. Analytical expressions, for the case of non-stationary white-noise accelerations, were also derived. The present approach was different from conventional optimum design criteria since it was based on minimizing displacement as well as accelerating variance of the main structure responses without considering performances required against discrepancy in response. In this study, in order to control the tremor induced on biomechanical arm model excited by non-stationary based acceleration random process, multi-objective optimization (MOO) design of a vibration absorber was developed and performed using modern imperialist competitive optimization algorithm for multi-objective optimization. The results demonstrated importance of this method and showed that multi-objective design methodology provided significant improvement in performance stability and giving better control of the design solution choice.