Fuzzy　neural　networks　(FNNs)　integrating　the　advantages　of　fuzzy　systems　and　neural　networks　are　useful　techniques　for　nonlinear　system　modeling.　However,　how　to　determine　the　structure　and　parameters　to　guarantee　satisfactory　modeling　performance　still　remains　a　challenge.　In　this　study,　a　self-organizing　FNN　with　hybrid　learning　algorithm　(SOFNN-HLA)　is　developed　for　nonlinear　system　modeling.　First,　a　growing-and-pruning　constructive　scheme　is　proposed　based　on　the　network　learning　accuracy　and　the　rule　firing　strength.　New　fuzzy　rules　can　be　developed　with　appropriate　initial　parameters　based　on　the　idea　of　an　error-correction　algorithm　to　improve　the　learning　performance.　Meanwhile,　some　redundant　rules　with　low　firing　strength　would　be　pruned　to　ensure　a　compact　structure.　Second,　a　hybrid　learning　algorithm　combining　an　improved　second-order　algorithm　and　the　least　square　method　is　developed　for　parameter　adjustment.　In　this　hybrid　learning　algorithm,　linear　parameters　and　nonlinear　parameters　are　tackled　separately　to　enhance　the　learning　efficiency.　Finally,　the　effectiveness　of　SOFNN-HLA　is　validated　by　two　benchmark　simulations　and　one　real　problem　from　wastewater　treatment　processes.　The　results　show　that　the　proposed　SOFNN-HLA　can　achieve　desirable　generalization　performance　with　a　compact　structure　for　nonlinear　system　modeling.　©　2023　Elsevier　Inc.