To　predict　the　effluent　ammonia　nitrogen　(NH4-N)　of　wastewater　treatment　process　(WWTP),　the　soft　computing　methods　are　widely　used,　in　which　the　mean　square　error　(MSE)　is　usually　adopted　as　the　performance　criterion.　However,　the　MSE　based　methods　cannot　fully　utilize　the　statistic　information　of　data　and　are　vulnerable　to　the　nonzero-mean　noise.　To　address　these　issues,　the　modeling-error　probability　density　function　based　fuzzy　neural　network　(PDF-FNN)　is　proposed　in　this　paper.　Firstly,　the　modeling　error　PDF　criterion　is　generated　to　minimize　the　spatial　deviation　between　the　modeling　error　distribution　and　the　predefined　target.　Then,　a　gradient　descent　method　with　adaptive　learning　rate　is　presented　to　update　the　parameters　of　PDF-FNN.　Furthermore,　the　convergence　of　PDF-FNN　is　analyzed　from　a　mathematical　point　of　view.　Finally,　a　nonlinear　system　modeling　and　the　effluent　NH4-N　prediction　in　WWTP　are　applied　to　prove　the　effectiveness　of　the　proposed　PDF-FNN.　The　results　indicate　that　the　PDF-FNN　has　better　prediction　accuracy　and　model　stability　than　other　methods,　especially　in　the　noisy　environment.　(C)　2020　Elsevier　B.V.　All　rights　reserved.