High-temperature superconducting (HTS) pinning maglev systems have emerged as promising solutions for high-speed transit, offering self-stability, simplicity, and reliability. These systems utilize the pinning effect between superconducting bulks beneath the vehicle and a permanent magnet guideway (PMG) to achieve levitation and guidance, with propulsion provided by a linear motor. However, the train is subjected to random excitations due to geometric and magnetic field irregularities of the PMG. While much of the existing research has concentrated on mitigating car body vibration for enhanced ride comfort, the issues related to frame vibration and the maintenance of consistent linear motor air gaps are still not fully addressed. This study introduces a secondary semi-active suspension device aimed at attenuating frame vibration in the HTS pinning maglev system. The research initially establishes a vehicle model based on an existing HTS pinning maglev test line and obtains track irregularity time-domain samples using the power spectral density (PSD) function. Classic semi-active control algorithms and the electromagnetic shunt damper (EMSD), enabling the implementation of semi-active control strategies, are then introduced. Subsequently, employing the groundhook linear (GH linear) control strategy, a vibration suppression model for the frame is established using the UM/Simulink co-simulation method. Finally, a comparison is made between the passive suspension system and the semi-active suspension system, with the Sperling index calculated to evaluate performance. The results affirm that this secondary semi-active suspension device not only significantly reduces frame vibration but also complies with ride comfort requirements, offering practical insights for future engineering applications.