Numerical modeling on the composite electromagnetic (EM) scattering from a two-dimensional (2-D) object located on a rough surface is presented by using the efficient method of fundamental solution (MFS). The proposed special choice of the MFS is an interesting alteative to the onerous mesh generation in the traditional numerical methods, particularly for the method of moment (MoM). There is no mesh scheme and singularity analysis, the field to be solved can be obtained directly in terms of the fundamental solutions of the appropriate wave equations. The numerical results are obtained and compared with the traditional MoM results, to demonstrate the accuracy and effectiveness of this technique.