A　high-order　accurate　artificial　boundary　condition　(ABC)　for　the　finite　element　analysis　of　near-field　wave　motion　problems　is　proposed.　The　out-of-plane　wave　propagation　problem　on　an　unbounded　exterior　domain　is　considered.　First,　an　exact　dynamic-stiffness　ABC　that　is　global　in　space　and　time　is　constructed　by　solving　the　initial　boundary　value　problem　of　a　far　field　using　the　separation　of　variables.　Second,　a　temporal　localization　method　that　consists　of　the　rational　function　approximation　and　the　auxiliary　variable　realization　is　developed　and　applied　to　the　dynamic-stiffness　ABC,　leading　to　a　high-order　accurate　ABC　that　is　local　in　time　but　global　in　space.　Third,　the　resulting　high-order　accurate　ABC　is　discretized　along　the　artificial　boundary　and　coupled　with　the　standard　lumped-mass　finite　element　equation　of　a　near　field.　A　symmetric　second-order　system　of　ordinary　differential　equations　in　time　is　obtained.　A　new　explicit　time　integration　algorithm　in　structural　dynamics　is　used　to　solve　this　system.　Finally,　numerical　examples　demonstrate　that　the　proposed　ABC　is　accurate,　efficient,　stable　and　easy　to　implement　into　the　existing　finite　element　codes.