In this article, a novel robust data-driven model-free predictive control framework based on the I/O data of the controlled plants, which is performed by incorporating the neural predictor-based model-free adaptive control and finite control-set model predictive control, is first proposed. The salient feature of the suggested framework is that the uncertainties, such as unmodeled dynamics and external disturbances, can be explicitly addressed in controlled systems. From a practical standpoint, however, the potential of this proposal is limited by a significantly increased online computational complexity, which makes it difficult to implement. To circumvent this limitation, a supervised imitation learning technique using data labeled is developed to imitate the known suggested controller, which the majority of the online computational burden can be transformed into offline computing by utilizing a trained artificial neural network subject to robustness characteristics. In particular, this development motivates a much simpler robust predictive control solution, which is convenient to implement in applications. Thus, by this proposal, the online implementation of much more complex predictive control strategies is made possible, and it explores a new possibility for future development of the complex control methodology. Finally, extensive simulative and experimental investigations for modular multilevel converter validate the interest and viability of the proposed design methodology.