Feedforward　neural　network　(FNN)　is　the　most　popular　network　model,　and　the　appropriate　structure　and　learning　algorithms　are　the　key　of　its　performance.　This　paper　proposes　an　online　self-organizing　algorithm　for　feedforward　neural　network　(OSNN)　with　a　single　hidden　layer.　The　proposed　OSNN　optimizes　the　structure　of　FNN　for　time-varying　system　including　structure　design　and　parameter　learning.　In　structure　design,　this　paper　measures　the　contribution　ratios　of　hidden　nodes　by　local　sensitivity　analysis　based　on　differentiation　method.　OSNN　merges　hidden　nodes　with　the　others　that　have　the　highest　correlation　when　their　contribution　ratios　are　almost　zero　and　adds　new　hidden　nodes　by　error　reparation.　For　parameter　learning,　an　improved　online　gradient　method　(OGM),　called　online　gradient　method　with　fixed　memory　(FMOGM),　is　proposed　to　improve　the　convergence　speed　and　accuracy　of　OGM.　In　addition,　this　paper　calculates　the　contribution　ratios　and　the　network　error　and　estimates　the　local　minima　by　using　the　fixed-sized　training　set　of　FMOGM　instead　of　one　sample　at　the　current　time,　which　can　obtain　more　effective　local　information　and　a　compact　network　structure.　Finally,　the　proposed　OSNN　is　verified　using　a　number　of　benchmark　problems　and　a　practical　problem　for　biochemical　oxygen　demand　prediction　in　wastewater　treatment.　The　experimental　results　show　that　OSNN　has　better　convergence　speed　and　accuracy　than　other　algorithms.