This paper deals with analyzing a novel eddy current damper for an axially magnetized multi-ring permanent magnet thrust bearing (MPMTB). Initially, the bearing is optimized for maximum axial force by selecting three general parameters (air gap, outer diameter of stator, and length) using a generalized optimization procedure. Then, the axial force of an optimized bearing is validated with the mathematical model results. Finally, the novel and conventional eddy current dampers (ECDs) for an optimized MPMTB are analyzed for damping forces and coefficients using three-dimensional (3D) finite element transient analysis in ANSYS. Based on the analysis results, the proposed novel structure could be selected to replace the conventional one for providing damping to MPMTB effectively without affecting the radial air gap between the rotor and stator rings.