This letter investigates the possibility of deploying a novel finite control-set model predictive control solution for solving the ongoing research challenges in predictive control regulated modular multilevel converter, i.e., model parameter sensitiveness and excessive computational burden as well as weighting factors selection. Specifically, it is realized by cascading a predictor-based neural network design, which enables a smooth and fast identification of system dynamics, and a computationally efficient finite-set predictive control, which is responsible for simplifying the rolling optimization and reducing the computational complexity. The main contribution of the proposed methodology relies on the fact that no knowledge of any model parameters and weighting factors in whole control process are required, which leads to a significant enhancement in the robustness and reliability of the control system in the presence of parametric uncertainties, while remaining computationally feasible. Finally, the stability analysis is given, and the proposed methodology is experimentally assessed for modular multilevel converter, where steady-state and transient-state performance tests confirm the interest of the proposal.