In this paper, a modified Lyapunov-function based control strategy for three-phase grid-connected LCL-filtered voltage source inverter is presented. The grid-connected system is modeled in the synchronously rotating frame. Lyapunov-function based control is derived from the Lyapunov's direct method which guarantees the global stability of the closed-loop system. Although the conventional Lyapunov-function based control strategy offers global stability, it is not able to damp the inherent oscillations that occur on the grid current. Therefore, a modified Lyapunov-function based control strategy is proposed by adding the capacitor voltage feedback into the control loop. In the proposed control strategy, the measurement of inverter currents, capacitor voltages and grid currents are essential. The generation of reference functions in the d- and q-components can be achieved by using the reference d-component grid current. Computer simulation results are presented and reported to validate the proposed control approach.