The propagation properties and scattering characteristic of a beam with orbital angular momentum transmission were researched by using the generalized Lorenz-Mie theory. Based on the research on the scattering of the Gaussian beam from single sphere，the intensity distributions of LGB beam at different propagation distance is analyzed. Without considering the relation between scattering and phase shift，the beam coefficients is obtained by the solution of scattering cross section，and the LGB is expanded in terms of the vector spherical harmonics as fundamental Gaussian beam. The scattering of the beam with orbital angular momentum from single sphere located on the propagation axis is studied. The influence of scattering intensity and angular distribution on scattering characteristic for different beam width is discussed by numerical simulation，and compared with those for the plane wave. The results show that when the beam waist radius is very small，the beam waist radius has serious influence on the decay rate. When the beam waist radius is relatively large，the influence is similar to that of plane wave.