Voltage　source　converter-based　high　voltage　DC　(VSC-HVDC)　grids　have　raised　high-speed　operation　and　high　reliability　requirements　for　relay　protection.　Firstly,　the　symbolic　expressions　of　the　line-mode　fault　component　voltage　traveling　wave　in　case　of　the　internal　and　external　faults　were　derived,　which　consist　of　the　traveling　wave　propagation　term　and　the　DC　line　boundary　term.　It　is　theoretically　demonstrated　that　(i)　the　index　for　the　traveling　wave　propagation　term　in　case　of　internal　faults　is　greater　than　that　for　the　external　faults,　and　(ii)　the　index　is　independent　of　fault　impedance.　Secondly,　the　Levenberg-Marquardt　(LM)　algorithm　was　introduced　to　extract　the　index　and　an　index-based　non-unit　protection　method　as　well　as　the　protection　scheme　was　proposed.　The　proposed　method　is　theoretically　robust　and　independent　of　fault　impedance　and　fault　type.　Finally,　in　the　simulation,　the　fitting　results　have　indicated　that　the　symbolic　expressions　are　correct　and　the　extracted　indices　are　effective　to　characterize　the　location　of　the　faults.　Numerous　fault　cases　of　different　fault　distances,　fault　impedances,　and　fault　types　have　demonstrated　that　the　proposed　protection　scheme　has　high　sensitivity,　high　operation　speed,　and　high　reliability.　The　proposed　protection　scheme　does　not　require　high　sampling　frequency.　©　2021　Chin.　Soc.　for　Elec.　Eng.