In　the　present　paper,　by　applying　the　Lang-Firsov　canonical　transformation　and　the　nonequilibrium　Green　function　technique,　we　investigate　joint　effects　of　the　electron-phonon　interaction　and　intralead　electron　interaction　on　the　differential　shot　noise　and　Fano　factor　through　a　vibrating　quantum　dot　weakly　coupled　to　Luttinger　liquid　leads.　The　influences　of　electron-phonon　coupling　and　intralead　electron　interaction　on　differential　shot　noise　and　Fano　factor　are　studied　in　detail.　Variation　of　the　main　resonant　peak　and　phonon　satellite　peaks　with　the　electron-phonon　interaction　and　electron-electron　interaction　of　the　leads　is　analyzed　numerically.　Besides,　we　also　reproduced　the　result　for　the　differential　conductance　derived　by　Skorobagat＇ko　and　Krive　using　the　master　equation.　(C)　2010　Elsevier　B.V.　All　rights　reserved.