A model predictive controller is designed to control thermal power in a nuclear reactor. The basic concept of the model predictive control is to solve an optimization problem for finite future time steps at current time, to implement only the first optimal control input among the solved control inputs, and to repeat the procedure at each subsequent instant. A controller design model used for designing the model predictive controller is estimated every time step by applying a recursive parameter estimation algorithm. A 3-dimensional nuclear reactor analysis code, MASTER that was developed by Korea Atomic Energy Research Institute (KAERI), was used to verify the proposed controller for a nuclear reactor. It was known that the nuclear power controlled by the proposed controller well tracks the desired power level and the desired axial power distribution.