This paper investigates the inherent damping characteristic of LCL- filters for three-phase grid-connected voltage source inverters. Specifically, it is found that when the converter-side current is used for implementing the feedback control, there will be an inherent damping term embedded in the control loop, which can neutralize the resonance introduced by LCL- filters. Theoretical analysis is then presented to suggest a general design guideline for choosing values of grid- and converter-side inductors, so that optimum damping can be naturally achieved by solely using converter current control, doing away with active damping, passive damping, or complex state observer. In cases where the design criterion is not fulfilled, the damping information contained in the converter current is extracted by a second-order notch filter, and then processed by a compensation gain to tune the system damping factor. The proposed compensation strategy requires no additional hardware and it will not cause an overmodulation problem due to its free of fundamental component. Both simulation and experimental results are finally provided to validate the theoretical findings developed in this paper.