In　this　work,　we　propose　a　theoretical　model,　a　series-coupled　vibrating　double-quantum　dots　adiabatically　connected　to　Luttinger　liquid　leads,　to　realize　the　controllability　of　quantum　interference　and　decoherence.　By　means　of　the　nonequilibrium　Green　function　approach　and　Lang-Firsov　canonical　transformation　technique,　we　investigate　the　effects　of　the　intralead　Coulomb　interaction,　interdot　tunneling,　and　electron-phonon　interactions　on　differential　conductance.　In　the　strong　dot-lead　tunneling　regions　the　antiresonance　features　of　destructive　interference,　Fano　interference,　and　negative　differential　conductance　(NDC)　appear　in　the　case　of　moderately　strong　intralead　Coulomb　interaction　and　electron-phonon　interaction,　and　they　can　coexist　under　appropriate　gate　voltages.　With　the　increase　of　the　intralead　interaction,　the　quantum　interference　is　first　enhanced　and　then　weakened,　and　eventually　decoherence　emerges,　leading　to　the　disappearance　of　the　intriguing　features.　In　the　weak　dot-lead　tunneling　regime,　there　appears　a　characteristic　pattern　of　positive　and　negative　differential　conductances.　It　is　stressed　that　there　is　no　requirement　of　the　asymmetry　in　this　system　for　the　occurrence　of　the　NDC　and　antiresonance　dip.　These　results　offer　an　understanding　of　the　structure　relationships　between　the　quantum　interference　effects　and　parameters,　which　enables　us　to　manipulate　the　quantum　interference　behavior　of　multi-functional　devices　in　the　future.