In this article, the control strategy is studied for the neutral-point-clamped three-level inverter-fed dual three-phase permanent-magnet synchronous motor (PMSM) drive with low switching frequencies. An interleaved finite-control-set model predictive control (MPC) scheme is proposed, where a two-layer MPC is designed to solve the multiobjective optimization problem. The two sets of windings in PMSM are sampled and controlled in an interleaved way so that the control delay and the prediction horizon of the drive system are reduced by half. Moreover, the proposed interleaved control scheme increases the equivalent sampling and control frequency from the perspective of the whole drive system, and thus provides better steady-state performance and dynamic performance. With the switching states of one inverter remaining unchanged, the cross traversal of vector candidate sets between two sets of windings is avoided, and the computational burden can be reduced effectively. Experimental results are given to verify the validity and effectiveness of the proposed interleaved control scheme.