Modulated model predictive control (M2PC) has recently emerged as a possible solution for control in starter generator systems in the more electric aircraft (MEA), due to its advantages of fixed switching frequency, fast response and good performance. However, conventional M2PC requires the prediction of each possible output voltage vector, which involves a heavy computational burden for the processor, especially for multilevel converters. This is an obstacle for practical industrial applications. To solve this problem this paper introduces a new, low-complexity modulated model predictive control (LC-M2PC) for a starter generator control system with a neutral point clamped (NPC) converter. The proposed LC-M2PC only needs prediction action once in each control interval, which can reduce the computational burden of processor. Fixed switching frequency is maintained and it can achieve a lower total harmonic distortion (THD) current than conventional M2PC, using space vector modulation (SVM). This proposed LC-M2PC method is validated on a prototype electrical starter generator (ESG) system test rig with three-level NPC converter. Experimental results verify the effectiveness of the proposed method.