Based on formula of vector wave functions in spherical and cylindrical coordinates and their transformation relations，a new method to solve beam coefficients of a two dimensions (2-D) on-axis Gaussian beam is provided. An analyzical expansion of beam coefficients is obtained. With the help of generalized Lorentz Mie theory，electromagnetic scattering by multi-layered spheres in a 2-D Gaussian beam is deduced. Distribution of scattering intensity changing with scattering angle are simulated. A comparison of scattering intensity with results of incident plane wave is given.