In this paper, a model-based current control (MBCC) approach with a compensating of dc-side inductor current ripple, active damping, and virtual time constant is proposed for single-phase grid-tied quasi-Z-source inverters with an LCL filter. The idea behind the ripple compensation is based on the inherent relationship between the ripple components of the dc-side inductor and capacitor voltages. It is shown that dc-side inductor current ripple can be compensated if the conventional simple boost control involving proportional-integral (PI) controllers is modified by subtracting the measured dc-side inductor voltage from the error signal of the first PI controller. Also, it is shown that the proposed MBCC causes the ac-side inverter current to track its reference in all circumstances. In addition, a virtual time constant is added to the control variable so that the dynamics of the ac-side inverter current can be adjusted as desired. Finally, in order to damp the LCL resonance, an active damping method is employed in the closed-loop system by modifying the ac-side reference inverter current. Experimental results are presented to show the validity and performance of the proposed control approach.