In vibration isolation systems, although large damping can effectively suppress the resonance peak, it will weaken the vibration isolation performance of the vibration isolation zone. For this reason, a Nonlinear Electromagnetic Damper (N-ED) based on a radially magnetized magnetic ring is proposed and investigated in this study. This N-ED uses different magnetization directions of the magnetic ring to achieve the nonlinear damping characteristics. Firstly, the radial magnetized magnetic ring is modeled and analyzed, and the validity of the model is verified by simulation, and the electromechanical coupling coefficient of the N-ED is calculated. Secondly, the relationship between voltage frequency and displacement frequency in the N-ED circuit was analyzed according to the coil motion law. Further, the amplitude-frequency response function of the N-ED is derived using the harmonic balance method (HBM), and the validity of the proposed N-ED is verified by comparing it with the numerical results; at the same time, its performance is analyzed in comparison with that of a linear electromagnetic damper. In addition, the study also explores the influence of the magnetic ring parameters on the electromechanical coupling coefficient and the influence of the negative resistance in the branch circuit on the vibration isolation performance and finally achieves the optimal parameter design.