Based on the generalized Lorentz-Mie theory（GLMT）

the incident fundamental Gaussian beam is expanded in terms of the vector spherical harmonics. The interaction of Gaussian beam with a multi Lagered sphere located on the propagation axis is analyzed. The modified algorithm for wave beam parameter gn and the recursive formulas as well as the computing procedure to calculate scattering coefficients an and bn are proposed. And the numerrical results are discussed and compared.