The purpose of this paper is obtaining an optimal arrangement of permanent magnets in a non-contact eddy current damper in order to achieve the maximum damping coefficient (c) among dampers with the same dimension. Magnetic theory and eddy current equations have been employed and solved by finite element numerical method. The dominant damping parameters and the optimum ratio of the ferrite core and the permanent magnet for the specific dimension have been achieved. A damper with the dimensions obtained from design is manufactured in order to verify the result of simulations. A setup also is designed and manufactured to verify the damping coefficient. The damping coefficient of simulation and experimental setup is 69.50 and 68.37 respectively which shows a close correlation between simulation and experiment results. The damping coefficient of the designed damper has been increased by 22.5% compared with a same dimension damper. Furthermore, frequency response is obtained by MATLAB software and a decrease of vibration amplitude in eddy current damper has been investigated. The result showed 20 dB reduction in the peak amplitude of frequency response in the designed damper.