In order to ensure the safe and efficient operation of the reactor while meeting the requirements of the power grid, it is necessary to follow and control the core power load according to the load demand, while suppressing the axial power deviation caused by changes in core power. Due to the correlation between core power load following and axial power deviation, the decoupling control method for the reactor has limitations, so it is necessary to control both objectives simultaneously. For complex reactor power control models, the performance of a single control method often has certain shortcomings, which cannot simultaneously meet performance goals such as response speed, robustness, and control cost. Therefore, it is necessary to design a multi-objective controller that combines multiple methods to control core power load following and axial power deviation. In the study, a two-point model of pressurized water reactor core power was established under the condition that the core power was divided into upper and lower parts. The LQR main controller designed based on the guaranteed cost control method using a two-point model has good response speed. To address the issues of strong model dependency and poor adaptability to uncertain parameters in the LQR controller, a sliding mode compensation controller is designed and combined with the LQR main controller to form an LQR-SMC multi-objective controller. Finally, the LQR-SMC multi-objective controller was tested through simulation experiments, and the simulation results showed that the multi-objective control method is feasible and has good control performance.