A load-following operation in APR+ nuclear plants is necessary to reduce the need to adjust the boric acid concentration and to efficiently control the control rods for flexible operation. In particular, a disproportion in the axial flux distribution, which is normally caused by a load-following operation in a reactor core, causes xenon oscillation because the absorption cross-section of xenon is extremely large and its effects in a reactor are delayed by the iodine precursor. A model predictive control (MPC) method was used to design an automatic load-following controller for the integrated thermal power level and axial shape index (ASI) control for APR+ nuclear plants. Some tracking controllers employ the current tracking command only. On the other hand, the MPC can achieve better tracking performance because it considers future commands in addition to the current tracking command. The basic concept of the MPC is to solve an optimization problem for generating finite future control inputs at the current time and to implement as the current control input only the first control input among the solutions of the finite time steps. At the next time step, the procedure to solve the optimization problem is then repeated. The support vector regression (SVR) model that is used widely for function approximation problems is used to predict the future outputs based on previous inputs and outputs. In addition, a genetic algorithm is employed to minimize the objective function of a MPC control algorithm with multiple constraints. The power level and ASI are controlled by regulating the control banks and part-strength control banks together with an automatic adjustment of the boric acid concentration. The 3-dimensional MASTER code, which models APR+ nuclear plants, is interfaced to the proposed controller to confirm the performance of the controlling reactor power level and ASI. Numerical simulations showed that the proposed controller exhibits very fast tracking responses.