This paper describes the application of semi-active variable stiffness damper (SAVSD) for response control of the seismically excited structure. The SAVSD consists of hydraulic damper connected in the form of bracing in a selected story of frame structure. The SAVSD changes its stiffness depending upon the structural response and accordingly adds the control forces in the structural system. In this paper, the comparative study and the performance of SAVSD under different ratios of damper stiffness to structural story stiffness is presented. The specific objective of this study is to evaluate the optimum value of damper stiffness ratio and its importance in structural response reduction. The optimum stiffness ratio is investigated for the structure subjected to four different types of earthquake ground motions. Here, the switching control law and newly proposed modified switching control law are used and the results are compared with uncontrolled and passive control cases. A numerical study is performed on five and ten-story shear building with different configurations of damper placement. The numerically evaluated optimum parametric values are considered for the analysis of the optimum damper placement in the structure. It is revealed that, the proposed modified switching control law is very effective in reducing the story displacements and inter-story drifts without increasing the top floor accelerations. The numerical results of various analyses indicate that SAVSD shows better performance over the passive dampers in reducing the structural responses.