In this work, a Lyapunov-function based control method for three-phase grid-tied LCL-filtered quasiz- source source inverters (qZSIs) is proposed. The mathematical model of grid-tied qZSI is modeled in the synchronously rotating dq-frame. Motivated from the energy distribution in qZSI, an energylike function (referred to as Lyapunov-function) is formed. Then, using Lyapunov's direct method a Lyapunov-function based control is described to guarantee the global stability of the closed-loop system. However, since the Lyapunov-function based control method involves a single-loop, its damping performance is not satisfactory. Therefore, the Lyapunov-function based control approach is modified by adding a second loop involving the capacitor voltage feedback into the control variable. The proposed control method requires the computation of ac-side reference inverter current and capacitor voltages which can be obtained by using the ac-side reference grid currents. The control of dc-side variables is achieved by using the traditional simple boost control technique. The generated shoot through state is combined with the pulse width modulation (PWM) signals generated from the proposed control method. Computer simulation results are presented to show the performance of the proposed control method in the steady-state and transients.