Purpose　The　finite　element　method　(FEM)　is　used　to　calculate　the　two-dimensional　anti-plane　dynamic　response　of　structure　embedded　in　D＇Alembert　viscoelastic　multilayered　soil　on　the　rigid　bedrock.　This　paper　aims　to　research　a　time-domain　absorbing　boundary　condition　(ABC),　which　should　be　imposed　on　the　truncation　boundary　of　the　finite　domain　to　represent　the　dynamic　interaction　between　the　truncated　infinite　domain　and　the　finite　domain.　Design/methodology/approach　A　high-order　ABC　for　scalar　wave　propagation　in　the　D＇Alembert　viscoelastic　multilayered　media　is　proposed.　A　new　operator　separation　method　and　the　mode　reduction　are　adopted　to　construct　the　time-domain　ABC.　Findings　The　derivation　of　the　ABC　is　accurate　for　the　single　layer　but　less　accurate　for　the　multilayer.　To　achieve　high　accuracy,　therefore,　the　distance　from　the　truncation　boundary　to　the　region　of　interest　can　be　zero　for　the　single　layer　but　need　to　be　about　0.5　times　of　the　total　layer　height　of　the　infinite　domain　for　the　multilayer.　Both　single-layered　and　multilayered　numerical　examples　verify　that　the　accuracy　of　the　ABC　is　almost　the　same　for　both　cases　of　only　using　the　modal　number　excited　by　dynamic　load　and　using　the　full　modal　number　of　infinite　domain.　Using　the　ABC　with　reduced　modes　can　not　only　reduce　the　computation　cost　but　also　be　more　friendly　to　the　stability.　Numerical　examples　demonstrate　the　superior　properties　of　the　proposed　ABC　with　stability,　high　accuracy　and　remarkable　coupling　with　the　FEM.　Originality/value　A　high-order　time-domain　ABC　for　scalar　wave　propagation　in　the　D＇Alembert　viscoelastic　multilayered　media　is　proposed.　The　proposed　ABC　is　suitable　for　both　linear　elastic　and　D＇Alembert　viscoelastic　media,　and　it　can　be　coupled　seamlessly　with　the　FEM.　A　new　operator　separation　method　combining　mode　reduction　is　presented　with　better　stability　than　the　existing　methods.