In this paper increasing the critical flutter wind speed of long-span bridges by using tuned mass dampers (TMDs) is theoretically and experimentally studied. Equations governing the motions of a bridge with TMDs are established. The Routh-Hurwitz stability criterion is used to study the aerodynamic instability of the bridge based on the characteristic equation of the system of the bridge and TMDs. A sectional model wind-tunnel test on the Tiger Gate Bridge, a suspension bridge with a steel box deck and a center span of 888 m, is carried out to confirm the numerical results. Some new findings from the test and the calculation are presented.