The basic principle of fast calculation of the Fredholm equation of the second kind based on Lanczos technique is introduced. The method of moments in conjunction with Lanczos technique is applied to predict the mono-static radar cross section (RCS) of an arbitrarily shaped two-dimensional dielectric cylinder. The electric field integral equation (EFIE) in the dielectric cylinder is established firstly, and then EFIE using the method of moments is changed into the matrix equation, and the electric field in the dielectric cylinder is obtained by solving the matrix equation using Lanczos technique. It is observed that the Lanczos technique can result in considerable CPU time saving.