Let　G　=　(V,　E)　be　a　graph,　V　(G)　=　{u(1),　u(2),...,　u(n)}　and　vertical　bar　E　vertical　bar　be　even.　In　this　paper,　we　show　that　M(L(G))　＞=　2(vertical　bar　E　vertical　bar-vertical　bar　V　vertical　bar+1)　+　Sigma(n)(i=1)　(f(G)(u(i))　+　g(G)(u(i))!!-n,　where　f(G)(u(i))-w(G-u(i)),　w(G-u(i))　is　the　number　of　components　of　G-u(i),　g(G)(u(i))　is　the　number　of　those　components　of　G-u(i)　each　of　which　has　an　even　number　of　edges,　and　M(L(G))　is　the　number　of　perfect　matchings　of　the　line　graph　L(G).　Also　we　show　that　M(L(G))　＞=　eta(Delta)　.　2(vertical　bar　E　vertical　bar-vertical　bar　v　vertical　bar-Delta+2)　for　every　2-connected　graph　G,　and　give　a　sufficient　and　necessary　condition　about　2-connected　graphs　G　such　that　M(L(G))　=　eta(Delta)　.　2(vertical　bar　E　vertical　bar-vertical　bar　v　vertical　bar-Delta+2),　where　eta(Delta)　=　Sigma(o　＜=　k　＜=Delta/2)(Delta/2k)(2k)!!,　Delta　is　the　maximum　degree　of　G,　and　(2k)!!　=　(2k-1)(2k-　3)...3.1.　(C)　2014　Elsevier　B.V.　All　rights　reserved.