A　Petersen　coil　was　used　as　a　passive　arc-suppression　device　(ASD)　to　mitigate　ground-fault　current　when　a　single-phase-to-ground　fault　occurred　in　distribution　networks.　However,　passive　ASDs　cannot　compensate　for　the　active　and　harmonic　components　of　ground-fault　current.　Furthermore,　a　massive　residual　ground-fault　current　would　endanger　human　life　and　the　reliable　operation　of　distribution　networks.　To　overcome　the　shortcomings　of　passive　ASDs,　a　three-phase　flexible　ASD　(FASD)　with　a　three-phase　cascaded　H-bridge　topology　was　presented.　A　three-phase　FASD　connected　to　a　bus　bar　of　distribution　networks　was　employed　to　compensate　for　the　ground-fault　current.　In　this　study,　the　FASD　with　the　backstepping　control　(BSC)　based　on　current-compensation　principle　was　proposed　to　completely　eliminate　the　ground-fault　current.　The　effectiveness　of　the　proposed　FASD　with　the　BSC　method　was　verified　using　the　simulation　and　experimental　results.