In　this　paper,　a　self-organizing　deep　belief　network　(SODBN)　with　growing　and　pruning　algorithms　is　proposed　for　nonlinear　system　modeling.　Although　deep　learning-based　DBN　has　been　widely　used　in　recent　years,　actually　more　detailed　researches　about　how　to　dynamically　determine　its　structure　are　seldom　observed　in　the　existing　literatures.　The　SODBN　can　automatically　determine　its　structure　using　growing　and　pruning　algorithms　instead　of　artificial　experience.　Firstly,　the　structure　of　SODBN　is　constructed　automatically　by　changing　the　number　of　both　hidden　layers　and　the　hidden　neurons　during　the　training　process.　The　self-organizing　strategy　is　implemented　by　automatic　growing　and　pruning　algorithm　(AGP),　which　is　actually　equivalent　to　adding　and　pruning　the　connecting　weights　between　neurons.　Secondly,　the　weights　are　dynamically　adjusted　during　the　process　of　structure　self-organization.　SODBN　is　able　to　adjust　the　weights　in　the　dynamic　process　of　self-organizing　structure,　and　is　helpful　to　improve　the　network　performances,　including　running　time　and　accuracy.　Finally,　the　proposed　SODBN　has　been　tested　on　three　benchmark　problems,　including　nonlinear　system　modeling,　water　quality　prediction　in　practical　wastewater　treatment　system　as　well　as　air　pollutants　concentrations　prediction.　The　corresponding　experimental　results　show　that　SODBN　has　better　performances　than　some　existing　neural　networks.　(c)　2018　Elsevier　B.V.　All　rights　reserved.