Seismic isolation systems are one of the most effective technologies for protecting structures from lateral loading, improving the seismic performance of the buildings against dynamic loads and base-isolated buildings have benefits in mitigating damage to the superstructure. Non-linear time history analysis is used to investigate the seismic response of fixed base and base-isolated building frames under far-fault ground motions and near-fault ground motions with fling step and forward directivity characteristics. Peak floor displacement, inter-story drift, absolute acceleration, base shear, and isolator displacement are some of the response characteristics that have been studied and examined as results of the analysis. The results demonstrated that using base isolators improves the seismic behavior of the used building, but it found that the isolator displacement is very large, during near-fault ground motion with the fling step effect particularly. For mitigating large isolator displacement during near-field earthquakes, the influence of a combination of the isolator and friction supplemental damper on the seismic response of a base-isolated 2D building frame is studied, and results demonstrated that using base isolators combined with viscous dampers can reduce the isolator's displacement.