A new concept of a “lower-bound transfer function (LBTF)” and a new frequency-domain optimal damper design method are presented. LBTF expresses an ideal performance for response control in the frequency domain under a constant sum of added damping coefficients (or the total cost of dampers). The effectiveness of the damper design for each mode can be captured visually through plotting the transfer function amplitudes of the model and the LBTF. An efficient generation method of LBTFs is also proposed. The proposed design method provides designs with multimodal adaptability (effective for multimodes). It does not require much computational load to implement the method since the optimization is conducted in the frequency domain, and the first-order or second-order sensitivities of the objective function can be derived analytically. The proposed design and the fundamental mode optimal damper placement are compared for shear-mass systems and moment-resisting frames through the transfer functions and the incremental dynamic analysis (IDA). It is demonstrated that the proposed designs effectively reduce the floor acceleration responses and the elastic deformation responses. Moreover, it is shown that the proposed designs can effectively reduce the elastic–plastic responses although the optimization is conducted for linear elastic models.