In　this　paper,　an　adaptive　second　order　algorithm　(ASOA)　has　been　developed　to　train　the　fuzzy　neural　network　(FNN)　to　achieve　fast　and　robust　convergence　for　nonlinear　system　modeling.　Different　from　recent　studies,　this　ASOA-based　FNN　(ASOA-FNN)　has　the　quasi　Hessian　matrix　and　gradient　vector　which　are　accumulated　as　the　sum　of　related　sub　matrices　and　vectors,　respectively.　Meanwhile,　the　learning　rate　of　ASOA-FNN　is　designed　to　accelerate　the　learning　speed.　In　addition,　the　convergence　of　the　proposed　ASOA-FNN　has　been　proved　both　in　the　fixed　learning　rate　phase　and　the　adaptive　learning　rate　phase.　Finally,　several　comparisons　have　been　realized　and　they　have　shown　that　the　proposed　ASOA-FNN　has　faster　convergence　speed　and　more　accurate　results　than　that　of　some　existing　methods.　(C)　2016　Elsevier　B.V.　All　rights　reserved.