This paper presents a modified MIMO sliding mode control (SMC) approach with constant switching frequency for single-phase grid-connected LCL-filtered quasi-z-source inverters (qZSI). In this approach, the sliding manifold is formed so as to achieve a concurrent SMC of both dC and ac side variables simultaneously. Such control is possible by generating the modulation signal and shoot through duty ratio. The constant switching frequency operation is achieved by smoothing the sliding manifold using a boundary layer. Cascaded PR controllers are employed to produce the ac side inductor current and capacitor voltage references alleviating the steady-state error in the grid current and tackling the damping issue. Dc side inductor current reference is produced by using power balance law in the circuit. Simulation results show the effectiveness of the proposed control approach.