Base-isolation system would undergo considerable great displacement subjected to strong earthquake. According to recent research progress，the hybrid control strategy combining variant tuned mass damper （VTMD） with base-isolation system has been proved to be effective in reducing such great displacement demand. However，large tuned mass is required to achieve better control performance，which may be difficult to realize in practical application. Employing the mass-amplification effect of the inerter device，a variant tuned mass damper inerter （VTMDI） is proposed in this study by inserting the inerter device in parallel with the dashpot in the VTMD and is attached to the isolation level in the base-isolated structure. Due to the stochastic nature of seismic ground motions，investigation into the optimum design of the VTMDI are conducted based on the framework of random vibration. It is demonstrated that the traditional optimization strategy，taking the inter-story drift of isolated superstructure as the optimization objective，is not cost-effective. Thereby，a novel optimization strategy consisting of two step optimization procedure is proposed. In this two-step optimization strategy，the optimization objective in the first step is taken as the control effect of the base-isolated structure equipped with the VTMDI compared with that of the corresponding base-isolated structure with the same dashpot，and then the optimization objective in the second step is to minimize the inter-story drift of isolated superstructure. And the dynamic time-history analyses show that both optimization strategies can effectively reduce the horizontal deformation in the isolation level and inter-story drift in the superstructure，and the excessive strokes of the tuned mass are also avoided. However，the two-step optimization strategy is more cost-effective than the traditional optimization strategy.