In　this　work,　the　transport　of　a　model　consists　of　two　quantum　dots　in　series　and　Luttinger　liquid　leads　is　researched.　The　motivation　is　to　reveal　the　interference　characteristics.　We　comprehensively　study　the　influence　of　the　intralead　Coulomb　interaction,　temperature,　detuning　levels　of　the　dots,　and　inter-dot　tunneling　on　transport.　By　applying　the　nonequilibrium　Green＇s　function　method,　a　general　current　formula　is　derived.　The　existence　of　the　intralead　interaction　leads　to　the　appearance　of　a　destructive　quantum　interference　anti-resonant　dip　at　the　zero-bias　voltage　of　the　differential　conductance.　The　gate-tunable　conductance　peaks　or　dips　depending　on　the　constructive　or　destructive　interference　are　demonstrated　when　the　energy　levels　of　the　two　dots　are　aligned.　While　when　the　energy　levels　are　misaligned,　the　intriguing　Fano　anti-resonant　interference　phenomenon　occurs.　These　results　offer　a　new　approach　for　designing　quantum　coherent　devices.