To investigate the effects of a trapezoidal sleeper track (TST) on the vibration and noise of rail transit viaducts, the wheel–rail interaction model was first built according to the vehicle–track coupling dynamics theory. Subsequently, the vibration responses of the viaduct were analyzed using the beam–slab finite element method, and its radiated noise was calculated using the acoustic boundary element method. The modeling method was verified based on the test data of a 3 × 40 m continuous rigid frame bridge. Taking the Jialing River Bridge of Chongqing Rail Transit Line 9 as the background, the control effects of the TST on the vibration and noise of the viaduct and the effective laws of different track parameters on the bridge noise were analyzed. Results show that the simulated and measured values are in good agreement; for example, the modeling methods are reliable; the radiated noise of the viaduct is influenced by the vibration responses under the action of train load, which are jointly determined by dynamic wheel–rail force (external excitation) and displacement admittance (self-vibration characteristics); compared with embedded sleeper track (EST), the TST can reduce the overall vibration acceleration level and sound pressure level of the box girder web plate by 13.9 dB and 7.8 dB, respectively; the stiffness of the damping path is the primary factor influencing the noise of the elevated box girder, followed by the sleeper thickness and the fastener stiffness; taking the bottom plate as an example, the stiffness of the damping pad is reduced by 1 and the overall sound pressure level can be reduced by approximately 3 dB; the sleeper thickness is increased by 1, and the overall sound pressure level can be reduced by 1–2 dB; and the fastener stiffness is reduced by 1, and the noise reduction is within 1 dB.