To improve the convenience of the traditional tuned mass damper(TMD), tuned inerter damper (TID) is proposed to mitigate the vibration of the structure subjected to ground white noise. The corresponding optimal damping parameter, optimal stiffness parameter and displacement variance analytical expression are deduced. The formulas show that the optimum parameters relate to the square of the mode difference between adjacent floors. The larger difference, the better control effectiveness. Then, TID is applied on three uniform structure and one non-uniform structure. The results indicate that TID performs well on the median and low buildings and it is also suitable for high mode control. TID-TMD works much better than TID in seismic reduction and when the structure is subjected to earthquakes exercitation, but they are neck and neck as a whole. So, TMD s only installed at the top floor with TID set up other floors, which solves the problems such as spatial occupation, inconvenient installment and heavy mass.