In the future, if nuclear power plants are used as a replacement for thermal power generation, the output power of the nuclear reactor should be able to adjust its power-peak flexibly like the thermal power plant while maintaining its internal stability. Considering the nuclear reactor’s structure, some of the variables cannot be measured directly, as well as issues with sensor measurement and system operation disturbances, a method that can accurately estimate the various state variables of the nuclear reactor is essential; To meet the practical application requirements, a controller with a simple structure that can flexibly adjust the nuclear reactor’s power according to loading tar-gets also has its value for researching. Therefore, in this paper, the square root cubature Kalman Filter (SCKF) was used as the state observer; To achieve the power regulating function while ensuring the system’s overall stability, the state-feedback Guaranteed cost controller (GCC) was designed combining with SCKF. In this article, the one point kinetics nonlinear model of the nuclear reactor power system which considering the thermo-hydraulic, Xenon and Iodine poison’s effect, was established to simulate the controlled object; The SCKF was designed based on this nonlinear model, and the fourth-order Runge–Kutta method was introduced to improve the CKF’s ac-curacy; The discrete-time GCC for the nuclear reactor core power system was designed based on the model’s linearization. The feasibility of SCKF’s estimating and the load-following function of the GCC designed in this paper was verified through numerical simulation.