An optimal Linear Quadratic Gaussian (LQG) control method under event-triggered sampling mechanism is proposed for the linear, discrete stochastic process with white Gaussian noise in networked stochastic system. Considering the joint design of optimum control law and optimum event-trigger law, it is proved that an optimal LQG control law based on event-triggered sampling mechanism can also satisfy the separation theorem. Then, performance cost function is derived, and based on which the optimum event-trigger law and the minimum value of the cost function are obtained by deterministic dynamic programming. Simulation results show that, compared with the optimal time-triggered LQG control under the same conditions, the proposed optimal event-triggered LQG control can save communication resources, decrease the transmission times, and improve the whole control performance at the same time.