Factors leading to poor control of the steam generator in a nuclear power plant are nonminimum phase characteristics, unreliable of flow measurements and nonlinear characteristics, which increase more at low power(below 20%) operation. And the study of problems for water level control in the steam generator is that design water level controller only power renge, not entire. This paper introduces a model predictive control(MPC) algorithm for solving poor control factors and quadratic programming(QP) for solving input constraints. Also presents the design method of stable model predictive controller in the entire power range. The simulation results show the efficiency of proposed MPC controller by comparing with PI controller, and effect of the design parameters.