For　an　undirected　and　weighted　graph　G　=　(V,　E)　and　a　terminal　set　S　subset　of　V,　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　[7],　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(|V|(2)|S|(3))　time　for　computing　a　2-vertex　connected　Steiner　network　(2V　SN)　whose　weight　is　bounded　by　two　times　of　the　optimal　solution　2-vertex　connected　SMN　(2V　SMN).　It　compares　favorably　with　the　currently　known　2-approximation　solution　to　the　2V　SMN　problem　based　on　that　to　the　survivable　network　design　problem　[10],　[16],　with　a　time　complexity　reduction　of　O(|V|(5)|E|(7))　for　strongly　polynomial　time　and　O(|V|(5)gamma)　for　weakly　polynomial　time　where　gamma　is　determined　by　the　sizes　of　input.　Our　algorithm　applies　a　novel　greedy　approach　to　generate　a　2V　SN　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(|V|(2)|S|(2)).　To　the　best　of　our　knowledge,　this　result　presents　currently　the　most　efficient　2-approximation　algorithm　for　the　2-connected　Steiner　minimal　network　problem.