In　this　paper,　a　novel　constructive　algorithm,　named　fast　cascade　neural　network　(FCNN),　is　proposed　to　design　the　fully　connected　cascade　feedforward　neural　network　(FCCFNN).　First,　a　modified　index,　based　on　the　orthogonal　least　square　method,　is　derived　to　select　new　hidden　units　from　candidate　pools.　Each　hidden　unit　leads　to　the　maximal　reduction　of　the　sum　of　squared　errors.　Secondly,　the　input　weights　and　biases　of　hidden　units　are　randomly　generated　and　remain　unchanged　during　the　learning　process.　The　weights,　which　connect　the　input　and　hidden　units　with　the　output　units,　are　calculated　after　all　necessary　units　have　been　added.　Thirdly,　the　convergence　of　FCNN　is　guaranteed　in　theory.　Finally,　the　performance　of　FCNN　is　evaluated　on　some　artificial　and　real-world　benchmark　problems.　Simulation　results　show　that　the　proposed　FCNN　algorithm　has　better　generalization　performance　and　faster　learning　speed　than　some　existing　algorithms.　(C)　2015　Elsevier　B.V.　All　rights　reserved.