Let　G=(V,E)　be　a　graph,　V(G)={u1,u2,⋯,un}　and　|E|　be　even.　In　this　paper,　we　show　that　M(L(G))≥2|E|-|V|+1+Σi=1n(fG(ui)+gG(ui))!!-n,　where　fG(ui)=dG(ui)-w(G-ui),　w(G-ui)　is　the　number　of　components　of　G-ui,　gG(ui)　is　the　number　of　those　components　of　G-ui　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))≥η(Δ)·2|E|-|V|-Δ+2　for　every　2-connected　graph　G,　and　give　a　sufficient　and　necessary　condition　about　2-connected　graphs　G　such　that　M(L(G))=η(Δ)·2|E|-|V|-Δ+2,　where　η(Δ)=Σ0≤k≤Δ/2(Δ2k)(2k)!!,　Δ　is　the　maximum　degree　of　G,　and　(2k)!!=(2k-1)(2k-3)⋯3·1.　©　2014　Elsevier　B.V.　All　rights　reserved.