Asphalt　concrete　(AC)　exhibits　significant　tension-compression　(TC)　asymmetry,　which　is　currently　not　considered　in　pavement　design.　This　study　develops　a　novel　temperature-dependent　dual　viscoelastic　model　to　quantitatively　capture　the　viscoelastic　behaviour　of　AC.　Unlike　the　conventional　viscoelastic　constitutive　model,　the　proposed　model　decomposes　strain　into　tensile　and　compressive　components　to　characterise　AC’s　TC　asymmetry.　Additionally,　a　systematic　modelling　framework　with　intrinsic　TC　asymmetry　is　developed　for　the　first　time　to　predict　the　response　of　pavement　under　moving　tire　load.　The　results　illustrate　that　implementing　the　proposed　dual　viscoelastic　model　enlarges　both　the　vertical　deformation　of　pavements　and　the　tensile　and　shear　strains　in　the　AC　layers,　bringing　it　closer　to　the　realistic　scenario　compared　to　the　conventional　model　that　only　considers　compression　properties.　Furthermore,　high　temperatures　and　low　vehicular　speeds　exacerbate　the　substantial　effects　of　AC’s　TC　asymmetry　on　asphalt　pavement.　This　study　provides　a　valuable　method　to　capture　AC’s　TC　asymmetry　and　predict　pavement　response　more　accurately,　giving　better　insight　into　pavement　response　and　enhancing　pavement　design　and　maintenance.　©　2024　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group.