The influence of single-particle scattering on the state transmission of orbital angular momentum (OAM) of Laguerre-Gaussian (LG) beams is studied by using the finite-difference time-domain method. The effects of particle size, particle position, ellipsoidal-particle-radii ratio, orientation angle and initial OAM mode of LG beams on the state degradation of OAM are investigated, respectively. The research results show that the larger the particle radius is, the more serious the OAM state degradation is. The change of the relative position between the scattering particles and the beam also leads to the regular change of the energy proportion. The initial OAM mode, ellipsoidal-particle-radii ratio and orientation angle all have influences on the state degradation at different extents.