LCL filter is commonly adopted in grid-tied inverters to eliminate harmonics produced by the pulse width modulation (PWM), because of its superior attenuation ability. However, it introduces potential resonance that is especially critical when connected to a weak grid with grid impedance varying. Practically, the active damping methods are popular in stabilizing the inverter system due to their flexibility and power loss-less, compared to passive ones. Active methods are mostly implemented with additional digital filters, power converters, control loops or/and sensors, complicating the system and increasing the costs. This paper provides an active damping method based on digital control delay (DCD) to ensure the stability of LCL-filtered inverters under the stiff or weak grid conditions. It is implemented with tuning the DCD to a proper region, which can be easily determined by method proposed in this paper. Finally, damping method is verified by simulation results in MATLAB/Simulink.