In traditional finite set model predictive grid-connected control of T-type three-level inverters, the lack of correlation between optimization processes in adjacent control cycles often leads to multi-cycle local optimality issues. To address this problem, this paper proposes a T-type inverter EMPC control strategy based on Voronoi-Softmax probability distribution, referred to as Voronoi-Softmax explicit model predictive control (VS-EMPC). First, a dead-zone linearization compensation strategy is adopted to correct the grid-connected model. Based on the concept of Voronoi diagrams, the online calculation of switching sequences is transformed into a Voronoi cell partitioning of the state space in the offline explicit model predictive control framework. During online operation, three candidate voltage vectors are obtained through a lookup table, and combined with an online Softmax probability exploration mechanism and adaptive dynamic coefficient calculation, the optimal candidate vector is selected through the guidance of the optimized probability distribution under multi-cycle correlation. Finally, a hardware-in-the-loop experimental platform is built to verify the proposed strategy, demonstrating favorable dynamic and steady-state performance, as well as its effectiveness in reducing storage requirements and achieving global optimal control.