In　this　paper,　we　study　the　two-dimensional　Helmholtz　scattering　problem　by　a　locally　perturbed　line　with　impedance　boundary　condition.　Different　from　the　problem　with　Dirichlet　boundary　condition,　the　Green　function　of　the　Helmholtz　equation　with　impedance　boundary　condition　becomes　very　complicated　and　comprises　surface　waves　along　the　locally　perturbed　line.　A　uniaxial　perfectly　matched　layer　(UPML)　method　is　proposed　to　truncate　the　half　plane　into　a　bounded　computational　domain.　The　main　contribution　of　this　paper　is　to　prove　the　well-posedness　of　the　PML　problem　and　the　exponential　convergence　of　the　approximate　solution　to　the　exact　solution　as　either　the　thickness　or　the　medium　parameter　of　PML　increases.