We　consider　a　numerical　solution　to　the　electromagnetic　obstacle　scattering　problem　in　three　dimensions.　Based　on　the　Dirichlet-to-Neumann　(DtN)　operator,　the　exterior　problem　is　reduced　into　a　boundary　value　problem　in　a　bounded　domain.　An　a　posteriori　error　estimate　is　deduced　to　include　both　the　finite　element　approximation　error　and　the　DtN　operator　truncation　error,　where　the　latter　decays　exponentially　with　respect　to　the　number　of　truncation　terms.　The　discrete　problem　is　solved　by　the　adaptive　finite　element　method　with　the　transparent　boundary　condition.　The　effectiveness　of　the　method　is　illustrated　by　numerical　experiments.