A large number of suspended algal particles exist in the underwater channels, which has a significant impact on the transmission characteristics of laser signals. Therefore, by the generalized Mie theory, a model for the scattering of Laguerre-Gaussian (LG) vortex beams by underwater suspended spherical algal particles is built. Specifically, numerical simulations of the effect of a single suspended spherical algal particle on the scattering characteristics of LG vortex beams are conducted, and the influence of the particle radius, beam waist radius, vortex beam order and topological charge on the differential scattering cross sections of LG vortex beams is calculated. Then, the influence of the underwater suspended spherical algal particle swarms on the differential scattering cross sections of LG vortex beams is further discussed. The results indicate that in the case of a single underwater suspended spherical algal particle, the differential scattering cross section increases with the increase in the particle radius, vortex beam order and beam waist radius, and decreases with the increase in the topological charge of vortex beams. Regarding the underwater suspended spherical algal particle swarm, the differential scattering cross section increases with the increase in the vortex beam order and beam waist radius, and decreases with the increase in the topological charge of vortex beams.