In　the　present　paper,　by　applying　the　Lang-Firsov　canonical　transformation　and　the　so-called　noncrossing-approximation　technique,　we　investigate　the　effect　of　the　electron-phonon　interaction　on　the　transport　of　a　quantum　dot　(QD)　system　in　the　Kondo　regime.　The　numerical　results　show　that　the　zero-frequency　shot　noise　and　Fano　factor　are　always　enhanced　significantly　due　to　the　electron-phonon　interaction.　The　well-known　peak　structure　around　the　Kondo　temperature　in　the　S-V　curve　exhibits　a　probe　of　the　electron-phonon　coupling　strength..　In　addition,　the　enhancement　of　the　Fano　factor　due　to　the　electron-phonon　interaction　is　attributed　to　the　reduction　of　the　Kondo-enhanced　density-of-state　and　transmission　probability　in　a　quantum　dot.　The　results　may　be　informative　for　future　experimental　measurements.　Copyright　(C)　EPLA,　2010