In this article, an efficient algorithm for the reconstruction of a 1-D random rough surface profile separating two lossy dielectric half-spaces is presented. First, the general scattering problem is formulated by the use of surface integral equations (SIEs). Then, the synthetic scattering field data are obtained through the use of these conventional SIEs. In the inverse problem, the same SIEs 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 in the sense of Tikhonov, and a least squares solution is obtained by the use of appropriate basis functions. A very detailed numerical assessment of the presented approach is provided which shows that the method is very effective and promising.