There are two major obstacles that prevent a conventional train from achieving high speed: the limitation of wheel–rail adhesion and the increase of instability in the wheel–rail running dynamics. To overcome these problems, a new hybrid train model is introduced in this study. This train utilizes a superconducting linear synchronous motor (SC-LSM), instead of a traction motor, for propulsion; therefore, this train does not have the limitation of adhesion between the wheel and the rail. Using an SC-LSM also improves the stability of the train during high-speed operations. The magnetic stiffness between the train and the guideway is additionally generated by using the SC-LSM, which is favorable for the running stability at a high speed. This study focuses on the magnetic stiffness and its effect on the running stability in the proposed hybrid train model. First, the magnetic stiffness in the SC-LSM is investigated both theoretically and experimentally. Then, a train dynamic model including the magnetic stiffness is developed and the effect of magnetic stiffness on the running stability is analyzed through various simulations.