Abstract: The vibration control effectiveness of the classical Tuned Mass Damper (TMD) is often limited by the size of its inherent tuning mass. However, the inerter, due to its energy dissipation enhancement and ability to provide virtual apparent mass, can significantly optimize and improve system performance when incorporated into the TMD system. This paper focuses on the optimization of tuning design parameters for two types of Single-connection Double Tuned Inerter Damper (SDTID). The transfer function for controlling the structural vertex displacement is established, and the optimal design formulas for each parameter based on the H norm optimization objectives are derived. Comparative analysis with traditional TMD shows that SDTID not only exhibits stronger vibration reduction capabilities but also significantly reduces the required damping coefficient. Through finite element case studies under seismic ground motion, the effectiveness of the SDTID designed by this method is further validated for both transmission tower structures and tower-line coupled systems. The research demonstrates that while achieving vibration reduction effects comparable to TMD, SDTID can reduce the inherent tuning mass by approximately 25% and lower the damping coefficient by up to 90%.