High-temperature superconducting (HTS) maglev system is promising to become the future high-speed transport due to its numerous advantages. However, the low-damping dynamic characteristics of superconductors make the system vulnerable to external disturbances, which present a significant challenge to its implementation. To enhance the vibration attenuation effect of the HTS maglev system, a non-contact damper that employs electromagnetic shunt damping (EMSD) and negative resistance is incorporated into the HTS maglev system. This study elucidates the principles of EMSD and negative resistance, and establishes the governing equations to describe the behavior of the HTS maglev model equipped with EMSD. Subsequently, the EMSD coupling coefficients are analysed via the finite element method (FEM) under varying conditions. Finally, a dedicated vibration test rig is designed and fabricated to validate the effectiveness of the proposed damper. The results demonstrate that the proposed damper, in combination with negative resistance, is capable of effectively suppressing vibration in HTS maglev systems. The maximum acceleration of the test model can be reduced by 86% compared with the original system without the damper. This work may provide valuable guidance for future practical implementations.