Aiming at the problems of long swing elimination time and slow positioning speed when lifting heavy objects, a Linear Quadratic Gaussian(LQG) controller based on optimal control theory and Kalman filter algorithm was proposed to suppress residual vibration. Firstly, the Lagrange equation was used to establish the nonlinear dynamic equation of the crane system. Secondly, the Jacobian matrix was used to linearize the nonlinear equation and the state space equation of the system was obtained. By proving the controllability and observability of the linear system, selecting the appropriate weight function, and designing the optimal Linear Quadratic Regulator(LQR) and the optimal state estimator, the LQG controller was obtained. The simulation of Simulink control system with relevant models shows that the designed LQG controller can effectively attenuate the residual vibration. Compared with PID controller, the proposed LQG controller can attenuate the residual vibration amplitude more effectively, the overshoot of vibration is smaller and the required steadystate time is shorter. The effectiveness and feasibility of the control strategy were verified.