The non-paraxial vector propagation characteristics of low order Laguerre-Gaussian beam (LGB) in space are analyzed by the space vector angular spectrum method, and the analytic expression of vectorial far-field distribution of LGB is obtained. Based on the generalized Lorenz-Mie theory, the scattering property of LGB by a single homogeneous spherical particle is analyzed. The research results show that, with the increase of topological charge of LGB, its hollow spot area increases while its on-axis differential scattering cross section decreases. With the increase of particle size, there exist peaks for the absorption, scattering and extinction efficiency factors, meanwhile these peaks shift towards the increase direction of particle size when the topological charge increases.