Recently,　a　polynomial　echo　state　network　(PESN),　an　extension　of　the　original　ESN,　was　proposed.　Its　polynomial　output　weights　were　augmented　by　the　high　order　information　of　full　input　features.　However,　there　may　be　noisy　and　redundant　features　to　construct　the　polynomial　function　as　the　output　weights,　which　results　in　the　high　computational　complexity　and　degrade　the　testing　accuracy.　To　eliminate　the　insignificant　features　and　reduce　computational　burden,　a　fast　feature　selection　method　in　polynomial　ESN　(FS-PESN)　is　presented.　Firstly,　a　feature　selection　criterion　is　utilized　to　choose　the　appropriate　features　to　construct　the　p-order　reduced　polynomial　function　as　the　output　weights　in　PESN.　Then,　an　iterative　strategy　is　given　to　reduce　the　training　computational　burden　in　FS-PESN.　Finally,　ten　benchmark　regression　data　sets　experiments　are　done　which　show　that　the　proposed　approach　can　obtain　better　prediction　accuracy　and　less　testing　time　than　the　PESN.