This paper tries to apply Sigma-Delta ADCs to inverter current sampling for active damping in voltage-controlled VSCs. The model of SD-ADCs is given and aliasing of current sampling with SD-ADCs is analyzed. An anti-aliasing synchronization method for average current sampling with SD-ADCs is proposed. Phase lag in the feedback loop caused by sinc filter is analyzed and optimal active damping coefficient is determined. Finally, simulation and experimental results validate the accuracy and effectiveness of the proposed method.