In　order　to　overcome　the　defects　of　gradient　descent　(GD)　algorithm　which　lead　to　slow　convergence　and　easy　to　fall　into　local　minima,　this　paper　proposes　an　adaptive　optimum　steepest　descent　(AOSD)　learning　algorithm　which　is　used　for　the　recurrent　radial　basis　function　(RRBF)　neural　network.　Compared　with　traditional　GD　algorithm,　the　adaptive　learning　rate　is　integrated　into　the　AOSD　learning　algorithm　in　order　to　accelerate　the　convergence　speed　of　training　algorithm　and　improve　the　network　performance　of　nonlinear　system　modeling.　Several　comparisons　show　that　the　proposed　RRBF　has　faster　convergence　speed　and　better　prediction　performance.　©　2017　Technical　Committee　on　Control　Theory,　CAA.