Analytical solutions to the scattering of a uniform uniaxial anisotropic sphere illuminated by an on-axis high-order Bessel vortex beam (HOBVB) are investigated. Using the vector wave theory, the expansion coefficients of the incident HOBVB in terms of the spherical vector wave functions (SVWFs) are obtained. According to the orthogonality of the associated Legendre function and exponential function, more concise expressions of the expansion coefficients are derived. It can reinterpret the incident HOBVB faster compared with the expansion coefficients of double integral forms. The internal fields of a uniform uniaxial anisotropic sphere are proposed in the integrating form of the SVWFs by introducing the Fourier transform. The differences of scattering characteristics of a uniaxial anisotropic sphere illuminated by a zero-order Bessel beam, Gaussian beam, and HOBVB are exhibited. Influences of the topological charge, conical angle, and particle size parameters on the angle distributions of the radar cross section are analyzed in detail. The scattering and extinction efficiencies varied with the particle radius, conical angle, permeability, and dielectric anisotropy are also discussed. The results provide insights into the scattering and light-matter interactions and may find important applications in optical propagation and optical micromanipulation of biological and anisotropic complex particles.