This paper analyzes first the stability of single-loop digital voltage control scheme for the LC-filtered voltage source inverters. It turns out that the phase lag, caused by the time delay of digital control system and by the use of integral controller, can stabilize the voltage loop without damping of LC-filter resonance. The stability regions are then identified with alternative voltage controller synthesized. For further widening the stability region, an active damping approach is proposed and co-designed with the voltage controller in the discrete z-domain. Simulations and experimental results of both 50-Hz and 400-Hz systems validate the theoretical analyses and the performance of the approach.