The　paper　concerns　the　numerical　solution　for　three-dimensional　electromagnetic　scattering　problems　in　a　two-layer　medium.　The　Cartesian　perfectly　matched　layer　(PML)　method　is　adopted　to　truncate　the　unbounded　physical　domain　into　a　bounded　computational　domain.　Although　the　PML　method　has　been　used　widely　to　solve　electromagnetic　scattering　problems,　rigorous　finite　element　error　analyses　are　still　rare　in　the　literature,　particularly,　for　electromagnetic　scattering　problems　in　layered　media.　This　paper　presents　a　thorough　error　analysis　for　finite　element　approximation　to　the　scattering　problems　in　a　two-layer　medium　with　PML　boundary　condition.　Numerical　experiments　are　presented　to　demonstrate　the　efficiency　of　the　PML　method　and　the　optimal　convergence　of　the　finite　element　solution.