In AC-DC power conversion, active front end rectifiers offer several advantages over diode rectifiers such as bidirectional power flow capability, sinusoidal input currents and controllable power factor. A digital finite control set model predictive controller based on fixed-point computations of an active front end rectifier with unity displacement of input voltage and current to improve dynamic response has been presented in this paper. Here by using a predictive cost function and fixed-point computations, the optimal switching state to be applied in the next sampling is selected. The low-cost architecture is implemented on a FPGA platform. Designed architecture is constructed based on fixed-point arithmetic with minimal functional units. The control algorithm, which is used in this architecture, is Finite-Set Model Predictive Control (FS-MPC). Compared with other controllers, this controller provides a much better dynamic performance. Finally, in order to evaluate the accuracy of the fixed-point computations several cases for various loading conditions and word lengths are verified.