In this paper, an effective finite-control-set model predictive controller (FCS-MPC) is proposed for an active dual output rectifier. The topology under study is a 5-level packed U cells (PUC5) rectifier. The optimized cost function is designed based on the capacitors' voltages and current errors. The Capacitors' reference voltages and the peak value of the reference grid current are used to normalize the errors within the cost function. The peak value of the current reference is generated by a PI controller using the capacitors' voltage errors. The presented results show a proper tracking of the rectifier's dual output voltages while ensuring a unity power factor.