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Single-phase ac-dc Power Factor Correction (PFC) rectifiers have attracted considerable attention in recent years due to the adoption of increasingly stringent power quality regulations. In this paper a nonlinear model predictive controller design for a single-phase Flyback PFC rectifier is presented. After approximation of the tracking error in the receding horizon by its Taylor-series expansion to a specified order, an analytic solution to the model predictive control (MPC) is developed and a closed-loop nonlinear predictive controller is introduced. The main advantage of this digital control method is that unity power factor can be achieved over wide input voltage, load current range and on high dynamics directly depend on the processing speed of microprocessor. This method is applied to a flyback PFC rectifier, can improve the voltage control dynamics. Simulation results show that flyback PFC rectifier with NMPC provides better and more accurate performance in both steady states and transient compared to linear control methods.