This paper presents a finite control set model predictive control (FCS-MPC) of a three-level bi-directional flying capacitor DC-DC converter for energy management application in a DC microgrid. The presence of three voltage levels give the converter advantage of having reduced voltage stress on the power switches and low ripple in its inductor current. Additionally, the capability of having bi-directional power flow enables the converter to integrate energy storage devices such as the battery to a DC microgrid effectively. An FCS-MPC algorithm is formulated using the developed mathematical model in order to yield the dual objective of bi-directional power flow and flying capacitor voltage balancing. Furthermore, a DC microgrid comprising photo-voltaic (PV) system, load, and battery are considered to assess the effectiveness of the designed FCS- MPC algorithm under varying load and PV power injections.