This　paper　presents　a　growing　algorithm　to　design　the　architecture　of　RBF　neural　network　called　growing　RBF　neural　network　algorithm　(GRBF).　The　GRBF　starts　from　a　single　prototype　randomly　initialized　in　the　feature　space;　the　whole　algorithm　consists　of　two　major　parts:　The　structure　learning　phase　and　parameter　adjusting　phase.　In　the　structure　algorithm,　the　growing　strategy　is　used　to　judge　when　and　where　the　RBF　neural　network　should　be　grown　in　the　hidden　layer　based　on　the　sensitivity　analysis　of　the　network　output.　In　the　parameter　adjusting　strategy,　the　whole　weights　of　the　RBF　should　be　adjusted　for　improving　the　whole　capabilities　of　the　GRBF.　In　the　end,　the　proposed　GRBF　network　is　employed　to　track　non-linear　functions.　The　computational　complexity　analysis　and　the　results　of　the　simulations　confirm　the　efficiency　of　the　proposed　algorithm.　©　2009　Springer-Verlag　Berlin　Heidelberg.