In　this　paper　we　investigate　the　joint　effects　of　the　electron-phonon　interaction　and　an　external　alternating　(ac)　gate　voltage　on　the　spectral　density　of　shot　noise　through　a　vibrating　quantum　dot　system,　by　applying　the　Lang-Firsov　canonical　transformation　and　the　Keldysh　nonequilibrium　Green＇s　function　(NGF)　technique.　We　find　that　the　effects　of　the　electron-phonon　and　electron-photon　interaction　on　the　differential　shot　noise　are　different.　The　main　resonant　peak　of　the　differential　shot　noise　is　decreased　only　when　a　time-dependent　gate　voltage　is　imposed　on　quantum　dot.　With　the　ac　field　amplitude　increasing,　the　main　resonant　peak　of　the　differential　shot　noise　decreases.　The　Fano　factor　of　the　system,　which　exhibits　the　deviation　of　shot　noise　from　the　Schottky　formula,　is　also　studied.　Super-Poissonian　shot　noise　appears　due　to　the　photon　absorption　(emission)　processes　in　the　low　bias　voltage　region.