Abstract: In order to restrain stick slip vibration of drill strings and bounce of drill bits, the movement mechanism of the stick slip vibration of drill strings and the bounce of drill bits was analyzed. According to Newton second law and the kinematics theory of electric drive system, the dynamic model and load model of the rotation system and lifting system of drill strings were established, and a state feedback controller for drill strings' rotation system and lifting system based on linear quadratic (LQR) control strategy was designed.The simulation results show that the LQR controller can stabilize the bit speed near the given rotary speed, and the response time of the control system is less than 25 seconds, which reduces the weight on bit, torque and fluctuation of axial displacement, and effectively restrain stick slip vibration of drill strings and bounce of drill bits.