Cavitation has been applied in medical treatments such as tissue ablation and lithotripsy. Considering that cavitation in medical applications always occurs within the fluid environment of the human body, which exhibits viscoelastic behavior, studying the dynamics of cavitation bubbles in viscoelastic media is essential for optimizing their medical use. This study used numerical simulations based on the open-source CFD platform OpenFOAM to develop a solver for compressible gas-liquid two-phase flows in viscoelastic fluid. Single cavitation bubble near a rigid boundary was simulated under various rheological parameters. Then the comparisons were made with corresponding cases in Newtonian fluid to analyze the effects of viscoelasticity on bubble dynamic characteristics. Results indicate that the viscoelastic effect inhibits the growth of cavitation bubbles and the intensity of the jet, and reduces the pressure load on the boundary caused by the cavitation process. Such influences are affected by the rheological properties of the fluid. As the relaxation time increases, the cavitation bubbles store more elastic potential energy in the early stage of growth and release it in the later stage, which prolongs the growth process of the cavitation bubbles and increases their maximum size. Conversely, when the migration coefficient increases, the energy dissipation during the growth of the cavitation bubbles increases, resulting in a decrease in their maximum size. Meanwhile, it is found that the velocity of the jet formed during the collapse of the cavitation bubble and the impact pressure on the boundary first increase and then decrease as the distance between the cavitation bubble and the boundary increases.This study can provide theoretical support for the application of cavitation bubbles in viscoelastic fluids and may inform both the beneficial use and mitigation of cavitation in fields such as chemical emulsification, seawater desalination, and petroleum transportation.