Liquid storage tanks (LSTs) can be efficiently protected from far-fault earthquakes by base-isolation. However, large isolation system and sloshing displacements may threaten the tank’s safety under near-fault earthquakes. Although the application of supplemental viscous dampers (VDs) at the base-isolation systems of LSTs located in near-fault areas may help, it may also increase superstructure demands under far-fault earthquakes. In addition to the characteristics of the earthquake, the isolation system and the superstructure properties may affect the success of base-isolated LSTs with supplemental VDs. Therefore, a numerical investigation is conducted in this study in order to determine the influence of the supplemental viscous damping ratio, the isolation system period, the tank wall flexibility, and the tank slenderness ratio on the seismic responses of base-isolated cylindrical steel LSTs with supplemental VDs including the base displacement, the sloshing displacement, and the normalized isolation system shear force under both near-fault and far-fault historical earthquake records. The tank is modeled by single-degree-of-freedom systems representing different modes on a common isolation basemat and the nonlinear dynamic analyses are carried out in 3D-BASIS-ME software. Findings show that while supplemental damping is required especially when LSTs with long-period isolation systems are subjected to large magnitude near-fault earthquakes, it may also cause amplifications in the sloshing displacement and isolation system shear force demands in case of far-fault earthquakes. Furthermore, it is determined that the influence of tank flexibility on both the superstructure and the isolation system responses is negligibly small while the tank slenderness ratio may have considerable effects.