In order to control the vibrations of wind turbine towers, a prestressed suspension-type inerter-based negative-stiffness damper (PSINSD) is proposed. The installation can be conveniently realized by a suspension cable connected to the primary tower. In order to achieve a better flexibility in frequency tuning, prestress is applied on the cable. The full-order nonlinear governing equations of the proposed PSINSD were established firstly. They were simplified to a reduced-order equivalent linear model for the convenience of analytical parametric optimization. Specifically, the optimal tuning was achieved via H-norm-based optimization approaches based on linearization. The negative-stiffness was optimized considering the balance of static and dynamic performances. Thus, a systematic practical optimal design approach for the proposed PSINSD was established. Finally, a practical example for the vibration control of a benchmark wind turbine tower was provided via nonlinear dynamic analysis with ANSYS software. Here, the inerter and negative-stiffness elements were implemented with linear matrix elements. And, the geometric nonlinearities of the cables were considered. The effectiveness of the proposed PSINSD and corresponding optimal design approach were validated. Consequently, the proposed approaches led to a high-performance, economic, and feasible passive vibration control for the wind turbine towers.