The arbitrary vector vortex beams on a higher-order Poincaré sphere (HOPS) are generated and manipulated using the combination of a Mach–Zehnder interferometer and a spatial light modulator. In terms of the transfer matrix method, the analytical expressions of the arbitrary vector vortex beams on the HOPS through a paraxial optical system are derived. The characteristics of the transformation of vector vortex beams by three typical optical systems, such as free space, Fourier transform, and fractional Fourier transform system, are investigated theoretically and verified experimentally. The intensity distribution of the vector vortex beams is found to be form-invariant under paraxial transformations. In addition, the intensity and polarization properties of the vector vortex beams are closely related to the several independent complex parameters of the beams and the optical systems. This research provides a reliable and flexible approach to manipulating the vector vortex beams in practical optical systems.