An analytic solution to the scattering of an arbitrary incidence Gaussian beam by a coated spheroidal particle is constructed by expanding the incident and scattered electromagnetic fields in terms of spheroidal vector wave functions. The unknown expansion coefficients are determined by a system of linear equations derived from appropriate boundary conditions. Numerical results of the normalized differential scattering cross section of the conducting and coated spheroidal particle are evaluated, and the scattering characteristics are discussed concisely.