Recently,　the　polynomial　echo　state　network　(PESN)　has　been　proposed　to　incorporate　the　high　order　information　of　input　features.　However,　there　are　some　redundant　inputs　in　PESN,　which　results　in　high　computational　cost.　To　solve　this　problem,　a　backward　learning　algorithm　is　designed　for　PESN,　which　is　denoted　as　BL-PESN　for　short.　The　criterion　for　input　features　removing　is　designed　to　prune　the　insignificant　input　features　one　by　one.　The　simulation　results　illustrate　that　the　proposed　approach　has　better　prediction　accuracy　and　less　testing　time　than　other　ESNs.　©　2019,　ICST　Institute　for　Computer　Sciences,　Social　Informatics　and　Telecommunications　Engineering.