Abstract: This paper proposes a Tuned Negative-stiffness Inerter Mass Damper （TNIMD） to mitigate seismic vibrations in prima? ry structures during earthquake excitation. The equations of motion for the coupled system of the primary structure and TNIMD are obtained using the Lagrange function， and fixed-point theory is applied for optimal design. The impact of negative-stiffness coeffi? cient on control performance is also discussed. Subsequently， a parametric analysis and evaluation of seismic vibration control are conducted. The results indicate that the displacement response of a primary structure equipped with the TNIMD is significantly less than those with a Vibration Tuned Mass Damper with Inerter （VTMDI） without a negative-stiffness spring. Furthermore， the smaller the mass and inertance ratios， the greater the advantages of TNIMD in vibration control， outperforming VTMDI. This confirms the requirement of installation limitations and the selection of a small mass ratio engineering. Additionally， seismic analy? sis shows the displacement and absolute acceleration of a primary structure equipped with TNIMD are superior to VTMDI under far-field， near field with pulse， and near-field without pulse earthquakes. The theoretical analysis and optimal design presented in this paper are suggested for engineering applications for seismic vibration control using TNIMD.