Deep　belief　network　(DBN)　is　one　of　the　most　feasible　ways　to　realize　deep　learning　(DL)　technique,　and　it　has　been　attracting　more　and　more　attentions　in　nonlinear　system　modeling.　However,　DBN　cannot　provide　satisfactory　results　in　learning　speed,　modeling　accuracy　and　robustness,　which　is　mainly　caused　by　dense　representation　and　gradient　diffusion.　To　address　these　problems　and　promote　DBN＇s　development　in　cross-models,　we　propose　a　Sparse　Deep　Belief　Network　with　Fuzzy　Neural　Network　(SDBFNN)　for　nonlinear　system　modeling.　In　this　novel　framework,　the　sparse　DBN　is　considered　as　a　pre-training　technique　to　realize　fast　weight-initialization　and　to　obtain　feature　vectors.　It　can　balance　the　dense　representation　to　improve　its　robustness.　A　fuzzy　neural　network　is　developed　for　supervised　modeling　so　as　to　eliminate　the　gradient　diffusion.　Its　input　happens　to　be　the　obtained　feature　vector.　As　a　novel　cross-model,　SDBFNN　combines　the　advantages　of　both　pre-training　technique　and　fuzzy　neural　network　to　improve　modeling　capability.　Its　convergence　is　also　analyzed　as　well.　A　benchmark　problem　and　a　practical　problem　in　wastewater　treatment　are　conducted　to　demonstrate　the　superiority　of　SDBFNN.　The　extensive　experimental　results　show　that　SDBFNN　achieves　better　performance　than　the　existing　methods　in　learning　speed,　modeling　accuracy　and　robustness.　(C)　2019　Elsevier　Ltd.　All　rights　reserved.