Modern super-tall buildings with rectangular floor shapes are vulnerable to significant vibrations due to the vortex shedding effect formed around structural edges. Tuned tandem mass dampers-inerters (TTMDI) is extended in this study to suppress vortex-induced responses of super tall buildings for occupant comforts. The optimal TTMDI tuning problem for a 400 m super tall building exposed to crosswind loads is solved through frequency-domain analysis. Meanwhile, the control performance of TTMDI is explored and contrasted with that of the tuned mass damper (TMD), tuned tandem mass dampers (TTMD) and tuned mass damper‐inerter (TMDI) from various perspectives. A crosswind-resistant design framework of the TTMDI equipped super-tall building system is then devised to meet comfort requirements. Finally, results are further assessed in the time -domain using a virtual real time hybrid simulation (VRTHS) system based on the proposed hybrid model predictive controller. It is found that there are several optimal inertance coefficient redistribution points (i.e. R points) in the design process and the R points have a great impact on the optimal internal structure of TTMDI. Results clearly demonstrate that TTMDI has better effectiveness and robustness than TMD, TTMD, and TMDI. Moreover, the total demand for total damping coefficients of TTMDI is significantly smaller than TMDI after the R points, indicating that it is easier to implement in engineering practices.