In this paper, a model predictive controller (MPC) is designed for a single-phase rectifier. The proposed MPC works with a continuous control set (CCS) that addresses variable switching issues in finite control set (FCS) MPCs. The observe-ability of the rectifier enables the design of a full-state observer to measure only output voltage in which the AC current of the rectifier is estimated. Both the proposed controller and observer are assessed with simulation studies and the results show the acceptable performance of the observer and CCS-MPC as well as good disturbance rejection in load and network parameter variations.