This paper presents the investigation of dynamic response of a guideway subjected to a maglev train moving with very high speeds. By using modal synthesis technology to establish the guideway-pier model, the equations of motion for the maglev train/guideway coupling system are derived and the dynamic response of the train-guideway system are computed using iterative methods. From the numerical studies of a 24m elevated guideway girder under a high-speed maglev train model of TR08, the results indicate increasing moving speeds may result in an amplified response of the guideway, and the second sub-resonance of the first mode of the guideway would be excited as well once the moving speed reaches around 350km/h. Furthermore, when the moving speed of the malgev train is higher than 400km/h, the response amplitudes of the guideway girder and moving vehicles are both amplified significantly. To avoid possible train-induced resonance of guideway vibration, the first natural frequency of the guideway should be designed to be higher than the characteristic frequency of the maglev vehicle/guideway system, which is equal to the ratio of the designed speed to the carriage length.