This article presents a seismic response of a two-way asymmetric building installed with a semi-active stiffness damper (SASD). The seismic response analysis of asymmetric structure is studied in terms of peak responses subjected to bi-directional excitations. The responses are obtained by numerically solving the governing equation of motion using state-space method. The effect of stiffness ratio and lyapunov constant on peak response which includes lateral, torsional displacement, and acceleration. The responses of asymmetric controlled and uncontrolled systems are simulated through MATLAB. To study the effectiveness of dampers, the controlled response of the asymmetric system is compared with the corresponding uncontrolled response. The parametric study indicated that the semi-active stiffness damper is quite effective in reducing various responses. Furthermore, on the optimum value of stiffness ratio, effectiveness of semi-active stiffness damper is reduced for lateral and torsional acceleration.