The　perfectly　matched　layer　(PML)　method　is　extensively　studied　for　scattering　problems　in　homogeneous　background　media.　However,　rigorous　studies　on　the　PML　method　in　layered　media　are　very　rare　in　the　literature,　particularly,　for　three-dimensional　electromagnetic　scattering　problems.　Cartesian　PML　method　is　favorable　in　numerical　solutions　since　it　is　apt　to　deal　with　anisotropic　scatterers　and　to　construct　finite　element　meshes.　Its　theories　are　more　difficult　than　circular　PML　method　due　to　anisotropic　wave-absorbing　materials.　This　paper　presents　a　systematic　study　on　the　Cartesian　PML　method　for　three-dimensional　electromagnetic　scattering　problem　in　a　two-layer　medium.　We　prove　the　well-posedness　of　the　PML　truncated　problem　and　that　the　PML　solution　converges　exponentially　to　the　exact　solution　as　either　the　material　parameter　or　the　thickness　of　PML　increases.　To　the　best　of　the　authors＇　knowledge,　this　is　the　first　theoretical　work　on　Cartesian　PML　method　for　Maxwell＇s　equations　in　layered　media.