CAT-1 is the first domestic magnetic confinement fusion device to use a magnetic levitation dipole field magnet design. Based on the overall goals and parameter design requirements of the CAT-1 device, this paper uses a simplified line current model, and employs vector magnetic field, mechanical equilibrium, and dynamics methods to complete the equilibrium stability analysis of the superconducting magnetic levitation system, and provides parameter design results. A simplified permanent magnet levitation experimental device has been preliminarily designed to verify the stability of the superconducting magnetic levitation system and the reliability of the parameters. The results show that for the CAT-1 device's levitation magnet weighing 1200 kg, current of 5 MA, and levitation distance of 2.0 m design goals, the optimal value of the lifting coil radius is 1.7 m, and the corresponding current is 3.49 kA. In order to effectively reduce and control the displacement of the levitated magnet, the working area near the equilibrium point should be restricted to vertical displacement |Δz| < 0.1 m, horizontal displacement |Δer| < 0.05 m, and tilt angle displacement |Δα| < π/24. The influence of TSR coil on the suspended coil is analyzed. The calculation shows that TSR and the suspended coil drift in the opposite direction, the drift amplitude is related to the radial position, and the originally closed magnetic field line on the side of the TSR coil is destroyed, resulting in the loss of the transported particles.A conceptual design of a levitation experiment device using 1.5 kg permanent magnets was completed, and the analysis showed that the distance between the permanent magnet and the copper levitation coil of 0.1 m, levitation coil current of 895A satisfying the requirements for control response speed.