This paper introduces a proportional-integral (PI) and sliding mode based control strategy for three-phase grid-tied three-level T-type quasi-Z-source inverter with LCL filter. The proposed control strategy has two parts. While the PI controller regulates the dc capacitor voltages and inductor currents in the quasi-Z-source network, the sliding mode control (SMC) achieves the grid current control. The proposed SMC removes the filter capacitor voltage requirement of phase c leading to simplicity in the implementation. In addition, for the sake of eliminating chattering, the sliding surface functions are passed through a boundary layer (smoothing) which removes the discontinuity and leads to fixed switching frequency operation. The validity of the presented control strategy is investigated by computer simulations during steady-state and transients caused by the reference change. It is shown that the dc capacitor voltage regulation is achieved and grid currents track their references.