There has been an increasing interest in using model predictive control (MPC) for power electronic applications. However, the exponential increase in computational complexity and demand of computing resources hinders the practical adoption of this highly promising control technique. In this article, a new MPC approach using an artificial neural network (termed ANN-MPC) is proposed to overcome these barriers. A power converter with a virtual MPC controller is first designed and operated under a circuit simulation or power hardware-in-the-loop simulation environment. An artificial neural network (ANN) is then trained offline with the input and output data of the virtual MPC controller. Next, an actual FPGA-based MPC controller is designed using the trained ANN instead of relying on heavy-duty mathematical computation to control the actual operation of the power converter in real time. The ANN-MPC approach can significantly reduce the computing need and allow the use of more accurate high-order system models due to the simple mathematical expression of ANN. Furthermore, the ANN-MPC approach can retain the robustness for system parameter uncertainties by flexibly setting the input elements. The basic concept, ANN structure, offline training method, and online operation of ANN-MPC are described in detail. The computing resource requirement of the ANN-MPC and conventional MPC are analyzed and compared. The ANN-MPC concept is validated by both simulation and experimental results on two kW-class flying capacitor multilevel converters. It is demonstrated that the FPGA-based ANN-MPC controller can significantly reduce the FPGA resource requirement (e.g., 2.11 times fewer slice LUTs and 2.06 times fewer DSPs) while offering a control performance same as the conventional MPC.