With the rapid development of smart materials, piezoelectric materials used as actuators in vibration isolation platform have been widely applied in precision machining, precision measurement and precision positioning, etc. This paper investigates active vibration isolation system of precision instrument based on four piezoelectric stack actuators, which is consisted of four bases, four piezoelectric stack actuators and precision instrument. Piezoelectric stack actuators are laid between the bases and precision instrument as active isolation components to suppress the vibration from the vibrating bases. Model of the active vibration isolation system is derived based on Newton's second law. Then the active controller is designed with LQR control algorithm. The simulation using MATLAB software show that this method is feasible and LQR controller designed can effectively suppresses the vibration of precision instrument.