This letter proposes a data-driven iterative learning predictive control architecture for power converters. The main objectives of this letter are to enhance the robustness and remain the high performance of finite control-set model predictive control (FCS-MPC) under unmodeled dynamics and parameter mismatch conditions. More specifically, an iterative dynamic linearization technique is utilized to equivalently reformulate the nonlinear power converter system at each operating point. Based on this, a model-free adaptive control scheme is presented to iteratively determine the optimal control actions. Due to the incorporation of iterative learning control and data-driven concept into the FCS-MPC framework, the effect of parameter perturbations can be alleviated in the proposed method, while creating a positive effect on the tracking error. Finally, a convergence analysis is provided and experimental investigations on a three-level neutral-point-clamped (NPC) converter confirm the effectiveness of the proposed method.