The　echo　state　networks　(ESNs)　have　been　widely　used　for　time　series　prediction,　due　to　their　excellent　learning　performance　and　fast　convergence　speed.　However,　the　obtained　output　weight　of　ESN　by　pseudoinverse　is　always　ill-posed.　In　order　to　solve　this　problem,　the　ESN　with　batch　gradient　method　and　smoothing　l0　regularization　(ESN-BGSL0)　is　studied.　By　introducing　a　smooth　l0　regularizer　into　the　traditional　error　function,　some　redundant　output　weights　of　ESN-BGSL0　are　driven　to　zeros　and　pruned.　Two　examples　are　performed　to　illustrate　the　efficiency　of　the　proposed　algorithm　in　terms　of　estimation　accuracy　and　network　compactness.　©　2019,　ICST　Institute　for　Computer　Sciences,　Social　Informatics　and　Telecommunications　Engineering.