We　investigate　the　interplay　of　quantum　interference　effects　and　the　electronic　correlation　on　the　transport　through　T-shaped　spinless　double　quantum　dots　coupled　to　Luttinger　liquid　leads　by　using　the　nonequilibrium　Green＇s　function　method.　We　find　that　the　weak　intralead　Coulomb　interaction　leads　to　a　zero-bias　antiresonance　dip　in　the　differential　conductance　for　small　interdot　tunneling　coupling,　which　is　distinct　destructive　interfer-ence　characteristic.　In　particular,　an　intriguing　Fano　antiresonance　profile　for　asymmetrically　coupling　to　the　Luttinger　liquid　leads　is　exhibited,　consistent　with　the　experiment　findings　but　different　physics　screening　origin.　The　strong　intralead　Coulomb　interaction　or　large　interdot　coupling　tunneling　quenches　the　quantum　interfer-ence　effects,　resulting　in　the　disappearance　of　Fano　antiresonance.　The　scaling　behavior　of　differential　conductance　on　temperature　is　presented　for　different　intralead　interactions.　The　relationship　between　destructive　interference　and　two-channel　Kondo　effect　is　given.　Our　results　provide　a　way　of　adjusting　in　and　out　of　antiresonance　to　achieve　quantum　interference　transistors　and　of　switching　by　tuning　the　gate　voltage　con-trolling　the　interdot　tunneling.