Herein, based on generalized Lorenz-Mie theory (GLMT), the scattering characteristics of single spherical aerosol particles illuminated by a high-order vector Bessel vortex beam are investigated. The electromagnetic field expression of each component of the Bessel vortex beam propagating along z axis in a rectangular coordinate system is transformed into an expression of each component in the spherical coordinate system. The beam factors of the Bessel vortex beam are calculated by the integral localized approximation method in GLMT, and then the scattering of single spherical aerosol particles illuminated by the axially-incident Bessel vortex beam is calculated. Taking the ammonium-nitrate spherical particles as examples, the distribution of variation in the scattering angle for the differential scattering cross-section of the interaction between aerosol particles and vector Bessel vortex beams which have different topological charges and half-cone angles are discussed by numerical calculation. Furthermore, variations of the extinction, absorption, and scattering cross-sections with the size parameters of uniformly spherical aerosol particles are discussed as well. Results show that, with increasing topological charge of the Bessel vortex beam, the differential scattering cross-section of particles gradually decreases; the absorption, scattering, and extinction cross-sections of the vector Bessel vortex beam with a certain topological charge overall trend to decrease as the half-cone angle of the beam increases.