Suspension bridges’ in-plane extended configuration makes them vulnerable to wind-induced vibrations. Vortex shedding is a kind of aerodynamic phenomenon causing a bridge to vibrate in vertical and torsional modes. Vortex-induced vibrations disturb the bridge’s serviceability limit, which is not favorable, and in the long run, they can cause fatigue damage. In this condition, vibration control strategies seem to be essential. In this paper, the performance of a tuned mass damper (TMD) is investigated under the torsional vortex phenomenon for an ultra-span streamlined twin-box girder suspension bridge. In this regard, the sensitivity of TMD parameters was addressed according to the torsional responses of the suspension bridge, and the reached appropriate ranges are compared with the outputs provided by genetic algorithm. The results indicated that the installation of three TMDs could control all the vulnerable modes and reduce the torsional rotation by up to 34%.