With the advantages of levitation/guidance self-stability, large levitation gap, and high lift-to-drag ratios, superconducting electrodynamic suspension (SC-EDS) train is becoming a viable candidate for the high-speed and ultra-high-speed rail transportation. In order to provide the basis for designing the optimization and control strategy, this paper establishes a comprehensive model for the SC-EDS train, which considers the dynamics of the bogie and car body in all directions. The obtained model reveals the complex coupling and feedback relationships among the variables, which cannot be described by the existing local models of the SC-EDS train. Simulation examples under different parameters and initial conditions are presented and discussed to demonstrate the potential use of the model given in this paper.