In two-dimensional (2D) electron systems, the viscous flow is dominant when electron-electron collisions occur more frequently than the impurity or phonon scattering. In this work, a quantum hydrodynamic model, considering viscosity, is proposed to investigate the interaction of a charged particle moving above the two-dimensional viscous electron gas. The stopping power, perturbed electron gas density, and the spatial distribution of the velocity vector field have been theoretically analyzed and numerically calculated. The calculation results show that viscosity affects the spatial distribution and amplitude of the velocity field. The stopping power, which is an essential quantity for describing the interactions of ions with the 2D electron gas, is calculated, indicating that the incident particle will suffer less energy loss due to the weakening of the dynamic electron polarization and induced electric field in 2D electron gas with the viscosity. The values of the stopping power may be more accurate after considering the effect of viscosity. Our results may open up new possibilities to control the interaction of ions with 2D electron gas in the surface of metal or semiconductor heterostructure by variation of the viscosity.