Currently, the Passivity-Based Control(PBC) has been used successfully in Grid-Connected Voltage Source Inverter(GCVSI) with L or LC filter. In practice, an LCL filter is widely used for the GCVSI. However, only a few papers have discussed how to apply the PBC for the GCVSI with LCL filter, where there is a complex structure in a three phase system due to using six state variables, and the variation of grid impendence is not addressed at the same time. In this paper, a PBC controller with only two state variables is presented. Furthermore, an active damping(AD) method is inserted into the control loop to resist the reverse effect of grid impendence variation, and to achieve a wide control bandwidth. The modeling and controller design are detailed described. The simulation platform is carried out in Matlab/simulink to verify the theoretical analysis.