Abstract: Tuned mass dampers are widely adopted in vibration control due to their simple mechanism, but their reliance on large additional mass limits their engineering applicability. Inerter technology utilizes apparent mass amplification to reduce the required tuned mass; however, the quantitative constraints for the lightweight design and, for the influence of key parameters on vibration mitigation performance remain unclear. This study proposes a pendulum-tuned mass inerter system (P-TMIS) that optimizes the coupling of pendulum structures and inertial components to enhance the lightweight capability and vibration mitigation efficiency of the system. A mechanical model of the P-TMIS is developed based on the Euler-Lagrange equation, and the equations of motion are derived to quantify the threshold of the apparent mass amplification factor, establishing a theoretical foundation for lightweight tuning. The research results demonstrate that: P-TMIS significantly reduces the required tuned mass, broadens the vibration control bandwidth, and exhibits robustness and stability under various operating conditions, providing a theoretical support and a practical guidance for the lightweight design and, for the efficient control of inerter technologies in complex vibration environments.