Abstract In this paper we propose an anisotropic Burgers equation with an anisotropic perturbation, which governs many nonlinear dynamic processes in an anisotropic diffusive (viscous) medium. Using conventional transformation methods, we find the analytical solution for the initial-value problem of the Burgers equation in a 2D anisotropic space. Based on the new development of the 2D Laplace’s theorem, we obtain the spatial asymptotic solution as the elements and determinant of the diffusive tensor approach zero. Finally, we also derive the temporal asymptotic solution as time goes to infinity for the 2D anisotropic Burgers system.