Based　on　the　systemic　investigation　of　recurrent　neural　network,　a　self-organizing　recurrent　radial　basis　function　(SR-RBF)　neural　network　which　based　on　the　spiking　mechanism　and　improved　Levenberg-Marquardt　(LM)　algorithm　is　proposed　in　this　paper.　The　hidden　neuron　in　the　recurrent　radial　basis　function　(RRBF)　can　be　added　or　pruned　by　computing　the　spiking　strength　of　the　connections　between　hidden　and　output　neurons　of　RRBF　neural　network.　Meanwhile,　to　ensure　the　accuracy　of　SR-RBF　neural　network,　the　parameters　are　trained　by　improved　LM　algorithm.　The　SR-RBF　neural　network　is　used　for　approximating　the　time-series　prediction　and　classical　non-linear　functions.　Finally,　comparisons　with　other　methods　demonstrate　that　the　SR-RBF　neural　network　is　more　effective　in　terms　of　accuracy,　generalization,　and　network　structure.