A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scat-tering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering patte can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing.