This paper proposes a super-twisting sliding mode control (ST-SMC) strategy for a three-phase grid-tied three-level T-type quasi-Z-source inverter (qZSI) with LCL filter. The qZSI topology used in this study offers a reduction in the capacitor voltages. While the dc capacitor voltages and inductor currents in the dc-side are controlled by conventional SMC, the grid current in the ac-side is controlled by ST-SMC. Unlike the existing methods, the use of SMC in the dc-side not only eliminates the need for using PI regulator, but also requires one gain only. The proposed ST-SMC in the ac-side controls the grid current successfully without using a special active damping method. Also, it eliminates chattering and leads to a fixed switching frequency operation. The validity of the proposed control strategy is investigated by computer simulations during steady-state and transients caused by the reference change.