This study investigates the wind-induced vibration response of TSSs under thunderstorm downbursts and introduces self-centering braces to analyze the vibration control. The study reveals that the vertical peak displacement of the upper chord nodes exhibits a “V” shaped distribution along the span direction, while the vertical residual displacement follows an “S” shaped distribution. The wind-induced vibration response at the cantilevered end is much stronger, and after the introduction of self-centering braces, the wind-induced vibration response significantly decreases, indicating that the self-centering braces play a noticeable role in controlling wind vibration. Additionally, the cable forces of the TSS significantly decrease under thunderstorm downbursts, with a loss of about 68%. The residual cable forces are uniformly distributed for the original structure and show a minor correlation with cable locations, whereas the residual cable forces of the structure with self-centering braces have a higher correlation with the cable locations. The residual cable force is significantly reduced after installing the self-centering braces, with a maximum reduction of 57.22%. Furthermore, the self-centering braces have a full hysteresis curve under thunderstorm downbursts, which indicates that it has high energy dissipation capacity and a good self-centering effect, which is conducive to controlling the wind vibration response of the structure under thunderstorm downbursts.