This paper investigates the feasibility and operability of a tuned mass damper (TMD) to control the lateral vibrations of a curved floating bridge. A curved floating bridge was designed with a bridge girder, 38 columns, and 19 pontoons, which was the same concept proposed for crossing Bjørnafjorden in Norway, except that the cable-stayed bridge was excluded in the present model. TMD was then attached to the mid-length of the bridge girder. Time-domain model was built to consider the girder-column-pontoon interaction based on the Cummins equation for pontoons and the lumped-mass line model for the bridge girder and columns, while TMD was modeled by the mass-spring-damper system. First, the genetic algorithm was employed to optimize the spring and damping coefficients of TMD at a fixed TMD mass under white noise wave excitations, and the fitness function was a summation of the standard deviation of the sway motion of 19 pontoons. Then, its feasibility was evaluated by comparing lateral vibrations and vertical bending moments with and without TMD under various combinations of wind/wave/current loads. Results demonstrate that TMD contributes to a reduction in the lateral vibration when resonance at the second wet natural frequency occurs, which can improve passenger comfort. Wind-induced lateral motions are significantly reduced at the second wet natural frequency while TMD has limited effects under other environmental loads. Moreover, bending moments are governed by higher modes mostly induced by storm waves, which cannot be controlled by TMD effectively.