Traditional model predictive control (MPC) for the induction motor fed by a three-level inverter needs to explore 27 voltage vectors to obtain the optimal one, which leads to high switching frequency and requires too much computation. To solve this issue, a low switching frequency model predictive control with partition optimization is proposed. First, the reference voltage vector can be gained from the prediction model at the next time, and the space voltage vector plane is divided into 12 sectors for further vector choice. Furthermore, considering inverter constraints, the candidate voltage vectors are determined according to the sector location of the reference voltage vector. In this way, the candidate vectors can be reduced to 3 at most. Then, a boundary circle limit is designed to avoid unnecessary switch changes. If the reference voltage vector is within the boundary limit, the switches do not act, which can reduce the system switching frequency without introducing the extra weight coefficient into the cost function. These selected voltage vectors are substituted into the cost function to determine the optimal one. Finally, the neutral point voltage deviation is controlled by the positive and negative redundant small vectors to realize the multi-objective constraint without weighting coefficients. The simulation results show that the proposed control method can significantly reduce the switching frequency; at the same time, both the dynamic and steady performances can be maintained well, and the cost function has no weight coefficients.