An　approach　for　solving　the　electrostatic　field　in　3-D　unbounded　domains　is　introduced　in　this　paper,　which　is　the　combination　of　the　finite　element　method　(FEM)　and　the　Kelvin　transformation.　The　principle　of　this　method　is　dividing　the　whole　infinite　region　into　two　parts　by　a　spherical　surface.　In　the　inner　part　with　a　sphere　as　the　boundary,　the　ordinary　finite　element　method　is　employed.　As　for　the　outer　open-boundary　part,　the　approach　first　transforms　it　into　a　finite　closed　domain　that　is　of　the　sphere　as　the　boundary,　in　which　the　transmuted　FEM　is　used.　It　is　allowed　that　the　exterior　open-boundary　part　is　of　non-uniform　medium,　such　as　unlimited　domains　or　different　shapes　with　different　materials　whose　interfaces　might　extend　to　infinity.