This paper presents the development and testing of a model-predictive control (MPC) for three phase (3φ) transformerless grid-connected 5-level power electronic converters (PECs). The proposed MPC employs a discrete-time model of 5-level PECs to predict the future values of the grid-injected currents and ground potential. predicted values of the grid-injected currents and ground potential are used to set the reference signals to minimize a cost function, which is formulated in terms of the command and actual grid-injected current and ground potential. The tested MPC is implemented for transformerless grid-connected diode-clamped and flying-capacitor 5-level PECs under different conditions. Test results show that the developed MPC can operate transformerless grid-connected PECs to ensure accurate, dynamic, and fast responses to changes in the power injected into the grid. Furthermore, the tested control demonstrates a good ability to minimize ground potentials during steady-state and step changes in the power delivered to/from the grid.