jats:pThe high-temperature superconductor (HTS) has been recognised as one of the most up-and-coming materials thanks to its superior electromagnetic performance (e.g., zero resistance). For a high-speed maglev, the HTS magnet can be the most crucial component because it is in charge of both the levitation and the propulsion of the maglev. Therefore, a fundamental study of HTS magnets for maglev is crucial. This article presents the fundamental design and modelling of the superconducting magnet for a high-speed maglev, including mechanics, electromagnetics, and loss analysis during instability. First, the measurements of the superconducting wire were performed. The HTS magnet was primarily designed and modelled to fulfil the basic electromagnetic requirements (e.g., magnetic field) in order to drive the maglev at a high speed. The modelling was verified by experimental tests on a scale-down HTS magnet. A more professional model using the H-formulation based on the finite element method (FEM) was built to further investigate some deeper physical phenomenon of the HTS magnet (e.g., current density and loss behaviours), particularly in situations where the high-speed maglev is in the normal steady state or encountering instability.</jats:p>