Controlling　the　quantum　interference　in　nanoscaled　systems　has　potential　application　for　the　realization　of　high-performance　functional　devices.　In　this　work,　the　quantum　interference　of　a　T-shaped　double-quantumdot　system　is　studied　in　detail　by　evaluation　of　differential　conductance　by　means　of　nonequilibrium　Green＇s　function　method.　The　factors　of　Coulomb　interaction　in　Luttinger　liquid　leads,　electron-phonon　interaction,　interdot　tunneling,　and　dot-lead　coupling　are　taken　into　account.　In　the　differential　conductance　curve,　there　appear　a　series　of　antiresonance　dips　due　to　phonon-assisted　destructive　interference　when　the　interdot　tunneling　is　weak,　and　they　can　coexist　with　zero-bias　antiresonance　dip.　When　the　dot-lead　couplings　are　asymmetric,　both　the　antiresonance　dip　and　Fano　line　shape　dip　can　occur　for　strong　dot-lead　coupling.　Our　results　also　show　the　coexistence　of　low-bias　negative　differential　conductance　and　Fano　antiresonance,　as　a　manifestation　of　the　interplay　between　strong　intralead　Coulomb　interaction　and　weak　dot-lead　coupling.　These　interference　phenomena　emerged　in　a　relatively　simple　model　promises　helpful　guidance　for　controlling　over　the　electrical　performance　of　interference-based　molecular　devices.