In　this　paper,　we　establish　a　model　to　realize　the　photon　-assisted　destructive　interference　phenomena,　the　model　consisting　of　parallel　-coupled　double　quantum　dots　and　Luttinger　liquid　leads.　By　applying　the　canonical　transformation　and　the　nonequilibrium　Green＇s　function　technique,　the　general　time　-dependent　current　formula　is　developed.　The　joint　effects　of　the　intralead　Coulomb　interaction　and　an　external　ac　field　on　the　quantum　interference　are　investigated.　For　weak　intralead　interactions,　besides　the　usual　photon　-assisted　tunneling　resonance,　there　are　two　types　of　photon　-assisted　tunneling　destructive　interference:　one　is　related　to　interdot　coupling　and　the　other　to　intralead　interactions.　For　moderately　strong　intralead　interaction,　the　photonassisted　sidebands　are　suppressed　and　the　differential　conductance　scales　as　a　power　law　in　bias　voltage.　In　particular,　we　show　the　multiphoton　absorption　and　emission　up　to　four　photons　in　an　electron　tunneling　process.　We　believe　that　the　photo　-assisted　destructive　interference　results　obtained　in　this　paper　are　instructive　for　future　experiments.