Abstract: The design of reactor power control system is closely related to the safety and economy of nuclear power plants. To improve its power control performance, a linear quadratic gaussian (LQG) controller for core power control was designed and optimized in a pressurized water reactor nuclear power plant in this study. Firstly, a nonlinear dynamic model of the reactor core was established through mechanism modeling, which consisted of the point kinetics neutron equation, the thermal dynamics equation and the reactivity equation. The reactivity equation ignores the iodine-xenon effect and considers the reactivity introduced by the control rod, the fuel Doppler effect and the coolant average temperature reactivity feedback. The nonlinear dynamic mathematical model was then linearized based on perturbation theory, and its state space model and transfer function were derived. Secondly, the LQG optimal control method was used to design the core power controller. Since the selection of the linear quadratic regulator (LQR) weight coefficients of the controller is subjective and requires high experience of the designer, and the selection efficiency is low, the optimal weight values are not always selected, while the nondominated ranking genetic algorithm with elite strategy (NSGA-Ⅱ) has better optimal global search capability. Therefore, in this paper, the NSGA-Ⅱ algorithm was used to optimize the weighting coefficients of LQR. the multi-objective optimization objective function of reactor power and control rod travel was established by using the time multiplied by absolute value integral of error (ITAE) evaluation index, and the multi-objective optimization of LQR weight coefficients of LQG controller was carried out based on NSGA-Ⅱ algorithm. The corresponding Pareto optimal solution set and corresponding LQG controller were obtained. In order to obtain the better reactor power control performance, the LQG controller with the weighting factor corresponding to the point with the smallest power ITAE index was used for core power control. Finally, the LQG controller designed in this paper was compared with the traditional PID controller for typical operating conditions, such as ±10%FP step change of load condition and ±5%FP/min linear change of load condition. The results show that both the LQG controller and the conventional PID controller can control the reactor power under the above conditions and have good control performance. However, compared with the conventional PID controller, the core power LQG controller with optimized weighting coefficients designed in this paper has significantly better control performance, with faster power control speed and smaller overshoot.