The　Echo-State　Network　(ESN)　is　a　robust　recurrent　neural　network　and　a　generalized　form　of　classical　neural　networks　in　time-series　model　designs.　ESN　inherits　a　simple　approach　for　training　and　demonstrates　the　high　computational　capability　to　solve　non-linear　problems.　However,　input　weights　and　the　reservoir＇s　internal　weights　are　pre-defined　when　optimizing　with　only　the　output　weight　matrix.　This　paper　proposes　a　Hybrid　Gravitational　Search　Algorithm　(HGSA)　to　compute　ESN　output　weights.　In　Gravitational　Search　Algorithm　(GSA),　Square　Quadratic　Programming　(SQP)　is　united　as　a　local　search　strategy　to　raise　the　standard　GSA　algorithm＇s　efficiency.　Later,　an　HGSA-SQP　and　the　validation　data　set　to　establish　the　relation　configuration　of　the　ESN　output　weights.　Experimental　results　indicate　that　the　proposed　configuration　of　HGSA-SQP-ESN　is　more　efficient　than　the　other　conventional　models　of　ESN　with　the　minimum　generalization　error.