In this paper, an algorithm to reconstruct one-dimensional impenetrable rough surface from the knowledge of scattering field is presented. The rough surface is considered as locally perturbed and the scattering field data are collected above the roughness in a simple non-magnetic medium considering Neumann boundary condition. First, the surface integral equation constituted via the Neumann boundary condition is solved and scattering field data are observed synthetically. Then, the same surface integral equation together with the data equation are solved in an iterative fashion to reconstruct the surface variation. In the numerical implementation, the so-called ill-posed inverse problem is regularized with Tikhonov method and a least-squares solution is obtained by using Gaussian-type basis function. Finally, numerical examples are carried out to illustrate effectiveness of the method.