A model predictive control method is applied to design an automatic controller for thermal power control in a reactor core. The basic concept of the model predictive control is to solve an optimization problem for a finite future at current time and to implement as the current control input only the first optimal control input among the solutions of the finite time steps. At the next time step, the second optimal control input is not implemented and the procedure to solve the optimization problem is then repeated. The objectives of the proposed model predictive controller are to minimize the difference between the output and the desired output and the variation of the control rod position. The nonlinear PWR plant model (a nonlinear point kinetics equation with six delayed neutron groups and the lumped thermal-hydraulic balance equations) is used to verify the proposed controller of reactor power. And a controller design model used for designing the model predictive controller is obtained by applying a parameter estimation algorithm at an initial stage. From results of numerical simulation to check the controllability of the proposed controller at the $5\%/min$ ramp increase or decrease of a desired load and its $10\%$ step increase or decrease which are design requirements, the performances of this controller are proved to be excellent.