The high-switching frequency operation is highly undesirable for multilevel inverters (MLIs) in electric transportation systems. In this article, a high-performance sequential model predictive control (SMPC) with reduced switching frequency is proposed for MLIs. The proposed SMPC is applied to a four-level inverter (FLI), in which the inverter ac current models are formulated by using the forward Euler integration method, whereas the inverter floating capacitor (FC) voltage models are formulated by using Heun's integration method. The use of Heun's method reduces the computational error of the FC's voltage, leading to a reduction in the number of switching transitions, thereby minimizing their tracking error. This process further leads to a reduction in their ripples with the available switching states. Also, it produces a lower current and voltage harmonic distortion while operating at a low switching frequency in comparison with conventional model predictive control (MPC) methods. The steady-state and transient performances of the proposed SMPC are demonstrated through the experimental studies on a dSPACE/DS1103 controlled laboratory prototype. The FLI's performance with the proposed SMPC is further analyzed in terms of average switching frequency, FC voltage ripple, total harmonic distortion, and computational burden. Finally, a comparative analysis of the proposed and conventional MPC methods is presented.