Until now, computational burden alleviation and stability issues for the three-phase four-leg converter has not yet been thoroughly investigated. However, compared to the conventional controllers, the implementation of predictive current control approach for 3-Ø, 4-L inverter suffers a large computational burden due to its additional fourth-leg. Motivated by this fact, this article provides an alternative predictive current control implementation for 3-Ø, 4-L inverter which offers reduced computational effort to achieve similar performance as the conventional FCS-MPC and ensures the global stability of the closed-loop system. To further understand the consequences of the developed control law, theoretical stability analysis has been carried out that links Lyapunov's direct method with the closed-loop system behavior. The outcome of the theoretical stability analysis demonstrates the global stability of the overall system which is later supported by the experimental results. With the proposed method, the number of possible voltage vectors required to obtain the optimal voltage vector in each sampling interval reduces from sixteen to five and thereby simplifies the prediction process. It is also derived that the Lyapunov function-based approach actually yields to the dead-beat control, which has not been previously highlighted in the previous papers. The current work also provides experimental results for different loading conditions (balanced and unbalanced) which further demonstrates the efficacy of the proposed method.