In this talk, we study the wave scattering problem by a locally perturbed step-like surface. The total field consists of the incident plane waves , the reflective waves by the unperturbed step , the radiative waves , and the corner-scattering field due to vertical part of the step. The computation of is very time-consuming even unfeasible in practice, since it is represented by the reference background Green’s function, which is very complicated and difficult to compute. We consider general incident waves and propose a circular PML method to solve the scattering problem. The PML-approximate problem is formulated as an interface problem on the truncated domain with homogeneous boundary condition. The method does not compute explicitly. We have established the error estimates between the exact solution and the solution of the truncated problem.