Small pressurized water reactors (SPWRs) have wide application prospects due to their high power density, good safety and economic performance, and flexible operation. However, the reactor core has strong nonlinear and time-varying characteristics, which makes it difficult to control, especially under the large load variable operating conditions with the traditional PID control. Therefore, it is necessary to propose a more effective method for the SPWR reactor core power control. In this paper, an H∞ robust core power controller is proposed and verified with the SPWR reactor core as the research object. Firstly, a nonlinear model of nuclear reactor core and a linearized state-space model were obtained through mechanism modeling and model linearization; Then, five power level states were selected to design the core H∞ robust controller respectively, and the weighting of the affiliation function was adopted to design the core H∞ robust controller for the full operating conditions. The simulation results show that the proposed H∞ controller is able to improve the performance of the core power control system at small variable loads, and the control effect is significantly better than that of the PID control system at large and fast variable loads. Therefore, the H∞ controller designed by applying the weighting of the affiliation function can overcome the shortcomings of the traditional PID control system which has poor control effect when it is far away from the designed operating conditions, and the proposed H∞ robust controller can significantly improve the robustness of the control system.