An　absorbing　boundary　condition　(ABC)　is　particularly　important　for　finite　element　simulation　of　wave　propagation　in　a　multilayered　medium.　In　this　paper,　a　spatially　and　temporally　local　high-order　absorbing　boundary　condition　is　proposed　for　scalar　wave　propagation　in　semi-infinite　multilayered　media.　A　semi-discrete　motion　equation　is　derived　by　discretizing　the　truncation　boundary　of　the　semi-infinite　domain　along　the　vertical　direction.　The　scalar　dynamic　stiffness　in　the　frequency　domain　for　a　single　degree　of　freedom　(DOF)　on　the　truncation　boundary　is　obtained　by　only　considering　the　first　mode　of　the　semi-infinite　domain.　The　scalar　dynamic　stiffness　is　expressed　as　a　continued　fraction　expansion　that　is　stable　and　converges　exponentially　to　the　exact　solution.　The　ABC　based　on　the　continued　fraction　for　a　single　DOF　on　the　truncation　boundary　is　established　by　introducing　auxiliary　variables.　The　proposed　ABC　is　always　stable　and　it　can　be　coupled　straightforwardly　with　the　existing　finite　element　method.　Since　it　is　spatially　decoupled　and　the　coefficients　in　it　are　easy　to　obtain,　the　proposed　ABC　is　convenient　to　apply　in　engineering.　Numerical　examples　demonstrate　the　superior　properties　of　the　proposed　method　with　high　accuracy,　high　efficiency,　and　good　stability.　©　2020　Elsevier　Ltd