Due to the discrete nature of switching in voltage source converters (VSCs), the finite control set‐model predictive control (FCS) can be a proper choice for using in the control system of VSCs. This paper introduces a constrained FCS‐based current controller (CFCS‐CC) to control VSC output currents. In the proposed CFCS‐CC, the objective function is the same as used in the traditional FCS‐based current controller (TFCS‐CC) and an additional constraint is considered to reduce the average switching frequency. Because only one objective function is used in the suggested current controller, it does not need tunable parameters or weighting factors. Design simplicity and low computational burden are the main advantages of the suggested approach. Because the reference current of shunt active power filters (SAPFs) contains harmonic components, SAPFs require a highperformance current controller. Therefore, the performance of the suggested CFCS‐CC is assessed on a three‐phase SAPF. The proposed current controller is implemented on field‐programmable gate array (FPGA). The results obtained from FPGA inthe‐ loop simulations and experimental verification show that the suggested CFCS‐CC provides a lower switching frequency while maintaining the overall performance of the TFCS‐CC, such as fast dynamic response and low total harmonic distortion