This paper presents a design process for viscoelastic dampers and a full-scale test of a 5-story steel structure with added viscoelastic dampers. The mechanical properties of viscoelastic dampers and the dynamic characteristics of the model structure were obtained from experiments, and the results were used in the design process. The additional damping ratios required to reduce the maximum response of the structure to a desired level were obtained first by the convex model. Then the size of dampers to realize the required damping ratio was determined using the modal strain energy method by observing the change in modal damping ratio due to the change in damper stiffness. The designed viscoelastic dampers were installed in the first and the second inter-stories of the model structure, and the system was excited by a hybrid mass driver located on the fifth floor. The experimental results indicated that after the dampers were installed the dynamic response of the full-scale model structure reduced as desired in the design process.