For　an　undirected　and　weighted　graph　G=(V,E)　and　a　terminal　set　SV,　the　2-connected　Steiner　minimal　network　(SMN)　problem　requires　to　compute　a　minimum-weight　subgraph　of　G　in　which　all　terminals　are　2-connected　to　each　other.　This　problem　has　important　applications　in　design　of　survivable　networks　and　fault-tolerant　communication,　and　is　known　MAXSNP-hard　,　a　harder　subclass　of　NP-hard　problems　for　which　no　polynomial-time　approximation　scheme　(PTAS)　is　known.　This　paper　presents　an　efficient　algorithm　of　O(V2S　3)　time　for　computing　a　2-vertex　connected　Steiner　network　(2VSN)　whose　weight　is　bounded　by　two　times　of　the　optimal　solution　2-vertex　connected　SMN　(2VSMN).　It　compares　favorably　with　the　currently　known　2-approximation　solution　to　the　2VSMN　problem　based　on　that　to　the　survivable　network　design　problem],　with　a　time　complexity　reduction　of　O(V5E7)　for　strongly　polynomial　time　and　O(V5γ　)　for　weakly　polynomial　time　where　γ　is　determined　by　the　sizes　of　input.　Our　algorithm　applies　a　novel　greedy　approach　to　generate　a　2VSN　through　progressive　improvement　on　a　set　of　vertex-disjoint　shortest　path　pairs　incident　with　each　terminal　of　S.　The　algorithm　can　be　directly　deployed　to　solve　the　2-edge　connected　SMN　problem　at　the　same　approximation　ratio　within　time　O(V2S2).　To　the　best　of　our　knowledge,　this　result　presents　currently　the　most　efficient　2-approximation　algorithm　for　the　2-connected　Steiner　minimal　network　problem.　©　2012　IEEE.