Electromagnetic damping features non-contact operation, easy adjustability, convenient processing, and high energy consumption. Combined with the damping efficiency enhancement effect of the inertial system, it is conducive to further improving its damping effect. This paper proposes an inertial mass damper, named the Inertial Eddy Current Damper (IECD). The proposed IECD has the advantage of adjustability, meaning that the eddy current damping force can be adjusted by regulating the current in the coil. First, the mechanical model of the IECD was proposed through theoretical methods. Secondly, performance tests were conducted to verify the accuracy of the proposed mechanical model. Finally, numerical models of structures employing various applications of the IECD were established to conduct seismic response analysis. The results show that the proposed mechanical model effectively reflects the actual performance of the IECD. When used for energy dissipation and vibration reduction, the IECD demonstrates superior control performance in terms of displacement and velocity compared to the LVD, and the switch control strategy can address the issue of poor acceleration control performance. Combining the IECD with isolation bearings not only further reduces the seismic response of the superstructure but also enhances the safety of the isolation bearings, preventing excessive deformation.