It is widely demonstrated that the tuned mass dampers (TMDs) are efficient to suppress resonant vibration, but the effective bandwidth is narrow and the robustness of the system is not enough, especially applied to variable frequency excitation. This paper presents an optimization design method of multi-mass damper (MMD) for variable multi-frequency vibration control. The dampers mounted on the primary system are made up of one main TMD and two MMDs, and each MMD is made up of three mass dampers, whose damping is provided by magnetic dampers, whose analytical model is established for optimization. The optimization objective function proposed is based on the variance, the difference between the maximum and the minimum values, root-mean-square values of the primary system vibration, which can help attenuate the vibration and improve the robustness of the primary system theoretically. The simulation results indicate that the vibration of the primary system under multi-frequency is suppressed 6 dB by the designed dampers. In the experiments, the optimized damping ratios of every mass damper are realized using the magnetic dampers. The vibration amplitude of the primary system can be suppressed more than 50% when the main TMD and MMDs start work, the dramatic fluctuation of frequency response is replaced by gentle transition, and the experimental results are consistent with the simulation results well. [ABSTRACT FROM AUTHOR]