The　paper　concerns　the　numerical　solution　for　the　wave　propagation　problem　in　periodic　heterogeneous　media.　The　homogenization　method　is　utilized　for　the　solution　in　the　bounded　periodic　structure　with　highly　oscillating　coefficients.　The　perfectly　matched　layer　(PML)　technique　is　adopted　to　truncate　the　unbounded　physical　domain　into　a　bounded　computational　domain,　and　the　exponential　convergence　of　Cartesian　PML　is　generalized　to　the　Helmholtz　transmission　problem　in　periodic　heterogeneous　media.　An　efficient　adaptive　finite　element　algorithm　based　on　reliable　a　posteriori　error　estimate　is　extended　to　solve　the　homogenized　PML　problem,　and　the　reliability　of　the　estimator　is　established.　Numerical　experiments　are　included　to　demonstrate　the　competitive　behavior　of　the　proposed　method.