This paper proposes a Predictive Control, formally Dead-Beat (DBC), for a four-leg inverter having an Active Split DC-bus on the fourth leg and LC filters on phase-to-neutral outputs. Such a configuration permits to reduce the voltage ripple on the neutral point connected to inverter grounding. As only few control techniques have been investigated for Active Split DC-bus, the paper proposes to investigate the performance of DBC, which has been widely used for other power electronics applications. The main advantage of DBC over the classical PI or Resonant controller is that no tuning is required for control loop, while obtaining very fast transient response as well it can handle general constrained nonlinear systems with multiple inputs and outputs in a unified and clear manner. These features are highly valuable in power electronic converters used to supply the electrical utility loads in micro-grids. However, one of the main drawback of the DBC is the limited capabilities on harmonics compensations required when supplying unbalanced and non-linear loads. The paper presents continuous-time and discrete-time models of DBC applied to a four-leg VSI with Active Split DC-bus, highlighting the performance through simulation results as well as experimental tests.