The parameter optimization design and damping effect of the single-degree-of-freedom structure under the simple harmonic load by the MTVMD (multiple tuned viscous mass damper) are studied. The robustness of the system is analyzed when the structural parameters are changed. Taking the displacement and acceleration dynamic amplification factor as the optimization targets, the improved mode search method is used to search for the optimal parameters of MTVMD. The analysis shows that the increase of mass ratio and of sub-TVMD number, the damping performance of MTVMD is enhanced, and the structural robustness is enhanced when the structural parameters change. Considering the actual working state of the damper, the parameters may deviate from the optimal parameters. Assuming that the deviation of each sub-TVMD parameter obeys normal distribution, the Monte Carlo test method is used to compare and analyze the damping effectiveness and reliability of STVMD (single tuned viscous mass damper) and MTVMD in the most unfavorable deviation state of their parameters. Numerical results show that the damping effectiveness and reliability of STVMD are positively correlated with the number of sub-TVMD, while MTVMD has an optimal sub-TVMD number to make the damping effectiveness best. The damping performance of STVMD and MTVMD is negatively correlated with the maximum deviation rate of parameters.