The purpose of this investigation is to design a nonlinear pressurized water reactor (PWR) core load-following control system for regulating the core power level and axial power difference and to analyze the global stability of the system. In modeling a two-point–based nonlinear PWR core without boron, the power rod and axial offset (AO) rod are considered. The two points are the bottom half and top half of the core. When the power rod and AO rod are in the same point (case 1), the power rod is an input, and the core power level is an output. When the power rod and AO rod in the core are not in the same point (case 2), the power rod and the AO rod are two inputs, and the core power level and axial power difference are two outputs. For each case, linearized models of the core at five power levels are chosen as local models of the core to substitute for the nonlinear core model over the global range of the power level. For case 1, proportional integral derivative (PID) control is utilized to design a controller of every local model as a local controller of the nonlinear core. For case 2, inverse Nyquist array control with the linear matrix inequalities method and PID control are adopted to devise a decoupling compensator and a dynamic controller for every local model, and their combination is a local controller of the nonlinear core. Based on the local models and local controllers of each case, the idea of flexibility control is used to design a decent controller of the nonlinear core at a random power level. A nonlinear core model and a flexibility controller at a random power level compose a core load-following control subsystem. The combination of core load-following control subsystems at all power levels is the core load-following control system for every case. Two global stability theorems are deduced to show that the core load-following control systems for the two cases are globally asymptotically stable within the whole range of the power level. Finally, the core load-following control system for each case is simulated, and the simulation results show that the control system is effective.