A UV method with multilevel partitioning (UVMLP) is developed to solve electromagnetic problem. In this paper we demonstrate the technique to treat electromagnetic problem for large surface in a two-dimensional (2-D) problem. Using the multilevel partitioning (MLP), the decomposition preprocessing, and the matrix vector multiplication require CPU of O(N logN) per iteration with a smaller constant factor for matrix column multiplication than decomposition. The memory requirement is of O(N logN). We demonstrate the technique for a rough surface scattering problem with surface length up to 13,000 wavelengths and RMS height up to ten wavelengths. Computations are based on using PC with a single Pentium 4--2.4 GHz processor and 1 G RAM. For the case of 65,536 unknowns, it requires about CPU from 3.3 to 5.33 s per iteration and a total CPU of 3.9--14.3 min with 49--146 conjugate gradient iterations.