Finite-state predictive torque control (FS-PTC) of an induction motor (IM) drive has been widely investigated for two-level voltage source inverter recently. This control method suffers from high and variable switching frequencies in a wide range, due to the limited number of available voltage vectors of the power converter. In order to take advantage of multilevel inverter drives which offer the benefits of low harmonic distortion of the stator currents, torque ripple, and low switching frequency, this paper proposes the integration of the FS-PTC with a three-level neutral-point clamped (3L-NPC) inverter driven IM drive. The drawback inherited from the topology of 3L-NPC voltage source inverter (VSI), such as neutral-point voltage, is easily handled by treating it as a variable to the cost function. Similarly, apart from the inverter topology itself, the average switching frequency is reduced further, and is maintained almost constant over a wide speed range. The effectiveness of the proposed FS-PTC in terms of torque and flux responses, capacitor voltage balancing, and low average switching frequency is validated through experimental results.