To improve the energy dissipation efficiency of a planar eddy current damper (ECD), a nonlinear eddy-current inertial mass damper (NEMD) combining the rotary eddy-current damping with two-node inertial mass element based on ball screw mechanism is proposed in this paper. Overall conformations and working principles of the NEMD were well demonstrated. Through semi-theoretical and semi-numerical analysis, three-dimensional finite-element simulation analysis as well as mechanical performance test, axial force characteristics, and calculation method for rotary eddy-current damping of the NEMD were then obtained. A two-stage design method of the NEMD based on the semi-theoretical and semi-numerical analysis and three-dimensional electromagnetic finite-element simulation analysis was established. Results show that the double amplification of the inertial mass and the equivalent eddy-current damping coefficient of the NEMD was realized, which significantly improved the energy dissipation efficiency of the ECD. As the axial velocity of the NEMD increased, corresponding eddy-current damping force increased at the beginning, and then the eddy-current damping force began to decrease nonlinearly when the force reached a maximum. The computational accuracies of the semi-theoretical, semi-numerical analysis, and three-dimensional electromagnetic finite-element simulation analysis on the eddy-current damping could basically meet the design requirements of the NEMD.