In this article, a band-limited three-level modulation scheme is proposed for a three-phase neutral-point-clamped (NPC) converter with an aim to balance the average capacitor voltages under all operating conditions. When conventional carrier-based pulsewidth modulation is applied, the amplitude of neutral point (NP)-voltage ripple tends to increase under linear imbalances, while the NP voltage can shift, leading to instability in the presence of nonlinear loads. A previously proposed three-level modulation scheme was able to eliminate all low-frequency capacitor voltage ripple by switching a phase between three levels in each switching period. This approach significantly increased the switching loss. The proposed modulation scheme limits the increase in switching loss by employing two operational bands, one fixed band applied to the capacitor voltages and another variable band applied to the phase currents. If the instantaneous capacitor voltages exceed the voltage band, then an appropriate phase-leg is switched in three levels to guarantee that the capacitor voltages cannot diverge further. If the instantaneous capacitor voltages reside within the voltage band, a variable current band is used to regulate switching in three voltage levels in order to obtain lower switching losses as compared to the conventional three-level modulation scheme. Therefore, the proposed modulation scheme presents a tradeoff between switching losses and capacitor voltage ripple. The experimental results are obtained under different loading conditions for validating the performance of the proposed modulation scheme.