Model Predictive Control (MPC) has attracted much attention and is widely used in power electronics. However, implementing the MPC algorithm is still a difficult task due to the fast dynamics of power converters and strict time constraints. In this paper, a computationally efficient MPC algorithm for grid-tied power converters based on the fast gradient projection method and invariant set theory is proposed. The algorithm is implemented and tested through hardware-in-the-loop simulations using Texas Instruments digital signal processors and Xilinx Field Programmable Gate Arrays platforms.