Model predictive control (MPC) is a powerful strategy for tackling multiobjective control challenges, but it often involves a laborious process of tuning weighting factors. This article proposes a gain-free MPC method for a recently developed nine-level T-type converter (9L-T2C), which offers advantages over traditional topologies, such as fewer components and improved efficiency. Drawing inspiration from Lyapunov's theory, this method avoids the use of weighting factors while effectively handling three targets, including current tracking, balancing of flying capacitors (FCs), and regulation of the neutral point (NP). Comparable with the traditional finite-control-set MPC (FCS-MPC), the proposed controller demonstrates high performance concerning all objectives. Additionally, it showcases superior resilience against model uncertainties when compared with the traditional approach. Experimental validation of the proposed MPC method is conducted in grid-connected operation under several conditions. The proposed method is subjected to a comparative analysis via the experimental implementation, where it is compared with a proportional-resonant (PR) controller and other state-of-the-art MPC methods. This analysis reveals the advantages of the proposed method, including eliminating the need for gains or weighting factors, improved robustness, and effective control of the FCs.