Multilevel converters have been turned into a prominent solution for high-power, medium-voltage applications. However, controlling multilevel converters is a complex task, which is typically implemented through single-input-single-output loops or via finite control set model predictive control (FCS-PC). Moreover, among the latest proposed multilevel converters, the five-level T-type nested neutral point clamped (5L-T-NNPC) stands out due to its reduced hardware requirements and wide voltage range applications. Although finite control set model predictive controller (FCS-MPC) has good performance with a fast dynamic response for operating this converter, this control strategy requires a detailed model of the converter, where parameter or model mismatch will degrade its performance. To improve the operation, this article proposes a novel model-free predictive control (MF-PC) that does not require a detailed model of the converter to operate, and it is robust under parameter mismatch. Indeed, it only requires the operation data of the converter to identify the parameters of a general autoregressive with exogenous (ARX) model via the least squares algorithm. Experimental and simulation results validate the better performance of the proposed MF-PC over the conventional FCS-MPC for a 5L-T-NNPC converter.