Seismic isolation devices are usually designed to protect structures from the strong horizontal component of earthquake ground shaking. However, the effect of near-fault (NF) vertical ground motions on seismic responses of buildings has become an important consideration due to the observed building damage caused by vertical excitation. As the structure needs to maintain its load bearing capacity, using the horizontal isolation strategy in vertical seismic isolation will lead to the problem of larger static displacement. In particular, the bearings may generate large deformation responses of isolators for NF vertical ground motions. A seismic isolation system including quasi-zero stiffness (QZS) and vertical damper (VD) is used to control NF vertical earthquakes. The characteristics of vertical seismic isolated structures incorporating QZS and VD are presented. The formula for the maximum bearing capacity of QZS isolation considering the stiffness of vertical spring components is obtained by theoretical derivation. From the static analysis, it is found that the static capacity of the QZS isolation system with vertical seismic isolation components increases when the configurative parameter reduces. Seismic response analyses of the seismic isolated structure model with QZS and VD subjected to NF vertical earthquakes are conducted. The results show that seismic responses of the structure can be controlled by setting the appropriate static equilibrium position, vertical isolation period, and vertical damping ratio. Adding a damping ratio is effective in controlling the vertical large deformation of the isolator.