Based on the extended boundary condition method, a semi-analytical solution to the scattering of an on-axis Gaussian beam by an arbitrarily shaped uniaxial anisotropic object is constructed. For the on-axis incident Gaussian beam, scattered fields as well as internal fields are expanded in terms of appropriate spherical vector wave functions, and the unknown expansion coefficients of the scattered fields are determined by using Schelkunoff's equivalence theorem and continuous boundary conditions. Numerical results of the normalized differential scattering cross section are presented, and the scattering characteristics are discussed concisely.