Abstract: A MoM-UV fast numerical algorithm based on multilevel UV matrix decomposition is presented to analyze the electromagnetic scattering from three-dimensional anisotropic impedance surface. The surface equivalence principle is adopted with electromagnetic current expanded by three-dimensional Rao-Wilton-Glisson(RWG) vector basis functions. The electromagnetic simulation of anisotropic impedance surface is performed using impedance boundary condition (IBC), with the electromagnetic parameters characterized by surface impedance dyadic. As the current is solved by BICGSTAB iterative method, so compressions to the low-rank sub matrices are performed using multilevel UV technology to reduce the operation of matrix-vector product and memory requirement. Several typical examples are presented with numerical results compared to the Mie series or pure MoM solution to verify the accuracy and efficiency of the proposed algorithm.