Tuned mass damper inerters (TMDIs) are devices used to reduce unwanted vibrations and displacements in a structure. To maximize the effectiveness of TMDI, its parameters should be optimally adjusted. The design variables in the TMDI optimization problem are the mass (mtmdi), period (Ttmdi), damping (ctmdi) and inerter (b) of the TMDI system. TMDI’s parameters affect TMDI’s control performance. Uncertainty about the mass of the TMDI can have an impact on the effectiveness of the TMDI. In this study, a robust optimal design of the TMDI is proposed by taking into account the uncertainty in one of the parameters, the mass. The aim of the robustness analysis is to assess the impact of the variation of mass, one of its parameters, on the effectiveness of the TMDI. The robustness analysis is performed by connecting a TMDI to a 10-story building and using mass ratios between 5% and 30%. The effects of the obtained results on the structural displacement are analyzed. The numerical results show that an optimally designed TMDI can achieve satisfactory vibration reduction and stiffness.