In　this　paper,　a　self-organizing　fuzzy　neural　network　with　adaptive　gradient　algorithm　(SOFNN-AGA)　is　proposed　for　nonlinear　systems　modeling.　First,　a　potentiality　of　fuzzy　rules　(PFR)　method　is　introduced　by　using　the　output　of　normalized　layer　and　the　error　reduction　ratio　(ERR)　in　the　training　process.　And　a　structure　learning　approach　is　developed　to　determine　the　network　size　based　on　PFR.　Second,　a　novel　adaptive　gradient　algorithm　(AGA)　with　adaptive　learning　rate　is　designed　to　adjust　the　parameters　of　SOFNN-AGA.　Moreover,　a　theoretical　analysis　on　the　convergence　of　SOFNN-AGA　is　given　to　show　the　efficiency　in　both　fixed　structure　and　self-organizing　structure　cases.　Finally,　to　demonstrate　the　merits　of　SOFNN-AGA,　simulation　and　experimental　results　of　several　benchmark　problems　and　a　real　world　application　are　examined　for　nonlinear　systems　modeling　with　comparisons　against　other　existing　methods.　Some　promising　results　are　reported　in　this　study,　indicating　that　the　proposed　SOFNN-AGA　performs　better　favorably　in　terms　of　both　convergence　speed　and　modeling　accuracy.　(C)　2017　Elsevier　B.V.　All　rights　reserved.