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-quantum-dot　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.　©　2024　Elsevier　B.V.