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In this paper, the variable gain LQG controller (VGLQGC) is designed for enhancement of dynamic performance for stochastic nonlinear systems. At sampling points the state variables of nonlinear control system with correlated noise is estimated by utilizing extended Kalman filter (EKF). In every sampling interval, according to the estimated state variables the optimal control is obtained by variable gain linear quadric regulator (VGLQR) based on separation principle. The controller has been validated by applying it to control a double inverted pendulum which is an inherently unstable system. The simulation experimental results show that the new scheme can effectively improve the dynamic performance.