In this article, a quasi-constant switching frequency zero voltage switching (ZVS) control strategy is proposed for three-phase grid-connected inverters. Full ZVS range can be achieved for all the switches at any load, modulation index, and power factor using discontinuous pulsewidth modulation. No additional high-frequency sensor or auxiliary circuit is needed. The switching frequency is constant at steady-state. It does not change with the phase angle or the power factor, but it varies with the modulation index, grid RMS voltage, and current. The frequency can be easily calculated in a digital controller based on current ripple prediction instead of current zero-crossing detection. The turn-on loss is eliminated so the inverter can operate at a high switching frequency, especially by using wide band-gap devices. The conversion efficiency, power density, cost, and dynamic response of the inverter can all be improved. A 3.3 kVA experimental prototype using SiC MOSFETs interfacing 400 V dc link with three-phase 110 V ac grid is developed to verify the effectiveness of the proposed control strategy.