The structures are exposed to a significant amount of seismic energy released during large earthquakes. A base isolation system (BIS) is one of the most efficient solutions to mitigate seismic responses. However, only the BIS may not be sufficient as they can undergo increasing displacement demand in earthquake-prone zones due to the base isolators' inherent nonlinear behaviour. Supplemental viscous dampers and base isolation (BI) are one of the most effective ways to manage seismic responses while protecting the main structural system from permanent damage. The purpose of this study is to examine the effect of laminated rubber bearings (LRBs) stiffness change in the seismic reactions of an existing multi-story building with and without supplemental viscous dampers (VDs). To assess the effect of LRBs’ stiffness on the seismic performance of the building, three different stiffness ratios (i.e., the sum of the stiffnesses of the first-floor columns (k_1) to the sum of the stiffnesses of LRB (k_b)) were chosen, and these ratios 〖(k〗_1⁄(k_b)) were 20, 40, and 80. The Sosokan building, which is situated at Keio University in Yokohama, Japan, was selected as an example. The building model was developed in MATLAB and verified with experimental results. The effects of LRB stiffness were examined by employing linear time-history analysis, both with and without viscous dampers on the displacement of the isolation layer, inter-story drift, and acceleration of the building. In this study, it is found that the displacements and accelerations at isolation floor and above levels significantly reduce in the LRB base isolated system equipped with viscous dampers (BI&VDs) as compared to BI (no VDs) model. Also, it is concluded that a proper damping coefficient (Cd) is important for the reduction of both displacement and acceleration at the same time. The finding of this study shows the importance of an optimal damping coefficient section in the adopted building model.