This investigation is to design a nonlinear pressurized water reactor (PWR) core load-following control system with self-stability for regulating the core power and axial power difference within a target band. A two-point–based nonlinear PWR core without boron and with a power rod and an axial offset rod is modeled. By proposing the gap metric of the core to qualify the core nonlinearity, the linearized multimodel single-variable core under case 1 (multivariable core under case 2) classified by two movable regions of the power rod is modeled. Linearized models of the core at seven power levels are chosen as local models of the core to substitute the nonlinear core model for each case. Based on H-infinity (H∞) control theories, the linear matrix inequalities method is adopted to design a H∞ output-feedback controller of every local model, which is a local controller of the nonlinear core of each case. In terms of the flexibility idea of control presented, the core load-following control system for each case is established. A theorem is deduced to analyze the global stability of the system of each case. Ultimately, simulation results show that the H∞ multimodel control strategy is effective for the core of each case.