The eddy current damper (ECD) has the characteristics of no contact and friction with the structure; unlike viscous damper, ECD has no problems, such as liquid leakage. First, the theory of planar ECD was introduced to investigate the performance of a planar ECD. Then, the reliability of the simulation method and the model for the planar ECD based on the software COMSOL was verified in accordance with the test on ECD coefficients. Finally, COMSOL was used to analyze the parameters of the planar ECD, such as conductive clearance, conductor thickness, conductor’s back iron thickness, and magnet’s back iron thickness. The planar ECD basically conforms to the assumption of viscous damping theory, and the results of damping coefficient simulation using COMSOL are also authentic. Thus, the conductive clearance and thickness of conductors have considerable influence on the damping coefficient, while the back iron thickness of the conductor and magnet has minimal influence.