Abstarct: In this research the effectiveness of active baxse isolation system on vibration response of multi degree of freedom construction has been studied. Using of baxse isolation system is one of the most effective ways for vibration control of construction and mitigation of this vibration.Using of passive baxse isolation can not be desirable because constructions occur under variable condition of lateral loading. Apply of active baxse isolation system is proper solution for this problem. Several algorithms is available for controlling of active systems, in this research hase been used of Linear Quadratic Regulator algorithm (LQR). First, hase been studied a five degree of freedom construction modeled by MATLAB in three states without baxse isolation, with passive baxse isolation and with active baxse isolation that have been occurred under two types of earthquakes near-field and far-field. Formulation has been done by matrix equations for without baxse isolation and with passive baxse isolation states, also formulation has been done by state space equations for with active baxse isolation state. Results indicate that active control system has desirable effect on vibration control of construction. Then for investigastion on performance of baxse isolation in high-rise structures, a fourteen degree of freedom construction has been studied. Results indicate that baxse isolation has not desirable effect on vibration control of high-rise structures. In this method (LQR) for calculation of weighting matrixes Q and R in each type of earthquake and model, have been done parameteric study on weighting matrixes and have been determined baxsed on desirable parameter of design.