Performance of a three-phase shunt active power filter (SAPF) relies on the capability of the controller to track the reference current. Therefore, designing an accurate current controller is crucial to guarantee satisfactory SAPF operation. This paper presents a model predictive current controller (MPCC) for a low-cost, four-switch, shunt active power filter for power quality improvement. A four-switch, B4, converter topology is adopted as an SAPF, hence offering a simple, robust, and low-cost solution. In addition, to further reduce overall cost, only two interfacing filter inductors, instead of three, are used to eliminate switching current ripple. The proposed SAPF model MPCC is detailed for implementation, where simulation and experimental results validate effectiveness of the proposed control algorithm showing a 20% improvement in total harmonic distortion compared with a conventional hysteresis band current controller.