Model predictive control (MPC) is a powerful control method for addressing multi-objective control problems, however, one of its main challenges is the cumbersome tuning process of the weighting factors. This paper presents a weighting factorless advanced MPC method for a recently developed nine-level active neutral point clamped (ANPC) converter, which has several advantages over conventional and recent nine-level topologies, such as low number of used switches and flying capacitors (FCs), reduced voltage rating of FCs and high efficiency. The developed MPC method avoids the use of weighting factors while addressing three control objectives: current control, FCs balancing and neutral point (NP) control. Similar to conventional finite-set MPC (FS-MPC), the presented method has high performance in terms of all control objectives. Moreover, this method exhibits enhanced robustness to parameter mismatch compared to the conventional scheme. The effectiveness of this method is validated through experimental testing under various operating conditions. The research demonstrates the potential for this technique to address control problems in ANPC-based converters and highlights its potential for further applications.