Suspension bridges are structures that because of their long span and high flexibility can be prone to ambient vibrations such as ground motions. They can experience high amplitude vibrations in torsional mode during an earthquake, where a vibration control strategy seems necessary. Recently, control systems have been widely used to mitigate vibration of structures. Tuned mass damper is a passive control system. Its performance and effectiveness have been verified both theoretically and practically. In this study, a tuned mass damper system is used to mitigate the torsional vibration of a suspension bridge. The Vincent Thomas suspension bridge is selected as a case study, and its response is reduced by a tuned mass damper under ten pulse-type records from 10 major worldwide earthquakes. By using sensitivity analysis, a parametric study is carried out to optimize tuned mass damper parameters, namely, mass ratio, gyration radius, tuning frequency, and damping ratio according to the maximum reduction of the response maxima. Finally, the optimum range of each parameter that can give the best performance and provide both operational and economic justification for the implementation of the project is suggested. The numerical results indicate that the optimized tuned mass damper system can substantially reduce the maximum response and vibration time.