In　three-phase　voltage　source　converters　(VSC),　the　widely　used　LCL　filter　can　always　achieve　an　excellent　attenuation　of　high　frequency　harmonics.　However,　the　resonance　peak　in　its　impedance　characteristic　as　well　as　some　extra　active　and　reactive　power　consumptions　of　the　RC　branch　is　inevitably　generated,　which　will　definitely　increase　the　complexity　of　the　filter　design　and　VSC　control.　The　output　character　of　a　passively　damping　LCL　filter　is　determined　by　only　three　parameters:　total　inductance　L,　damping　ratio　ζ　and　natural　frequency　ωn.　Actually,　different　combinations　of　the　three　parameters　can　produce　the　same　output　character.　Thus,　an　optimization　approach　is　essential　to　select　proper　values　for　each　element.　In　this　work,　detailed　analysis　of　a　passively　damping　LCL　filter　is　firstly　carried　out.　And　then,　the　optimization　process　is　implemented,　taken　the　lowest　active　and　reactive　power　consumption　of　the　RC　branch　as　the　target.　Hereafter,　the　design　principles　are　derived.　Finally,　the　proposed　analysis　and　design　approach　are　validated　by　the　experiments　of　different　filter　parameter　combinations.　©　2017,　The　editorial　office　of　Transaction　of　China　Electrotechnical　Society.　All　right　reserved.