The coupled resonance that occurs between a maglev vehicle and an elevated bridge is a unique problem for an electromagnetic suspension maglev system when the vehicle is suspended above the bridge without moving. This problem causes the bridge to vibrate in a large amplitude, it significantly degrades the ride comfort of the maglev train, and it needs to be solved before the commercial application of the system. In this paper, the principle of the stationary vehicle–bridge coupled resonance is investigated, and it is shown that the levitation system is non-passive and it causes self-excited vibration when the first resonance frequency of the bridge approaches the critical frequency of the levitation system. To eliminate the coupled resonance, an approach using a tuned mass damper (TMD) to render passive the levitation control system is presented, and it shows that a TMD with appropriate parameters can stabilize the coupled system. A procedure for seeking out a group of suboptimal parameters of the TMD is also proposed. This procedure ensures that the designed result has a satisfactory performance as well as a reasonable stability margin. The location where the TMD should be mounted to achieve the best performance is discussed. The numerical simulation shows that the designed TMD can completely suppress the vehicle–bridge coupled resonance.