In this paper, the effect of viscous dampers (VD) on the control of adjacent structures is firstly discussed, and then the tuned inerter dampers (TID) is utilized to enhance the control performance of adjacent structures. The relative displacement and absolute acceleration responses of the TID controlled adjacent structures are optimized and evaluated by the H∞ performance of the transfer functions. The results show that there is an optimal damping ratio to minimize the displacement response of the adjacent structure when VD is used, but the damping required corresponding to the optimal performance are relatively larger. Instead, the use of TID gradually enhances the control effect with the increase of inertance-mass ratio and the control effect of TID on the structure is more significant at small inertance-mass ratio. Compared with VD, TID only requires smaller damping to achieve a similar performance to VD.