A Poincaré sphere (PS) representation for states of polarization (SOPs) of vector vortex beams based on Jones matrix is proposed. For the vector vortex beams which are combined with two circular polarization optical vortexes of opposite topological charges, a distribution model of electric field vector is developed by using Jones matrix. Two influencing factors of SOPs are educed: the topological charge and azimuthal angle. And the PS representation for SOPs with different topological charges is presented. Compared with the higher-order PS constructed with Stokes parameters, the physical meaning of this description method for vector vortex beams is much clearer. After a rigorous vector Helmholtz equation analysis, the amplitude of vector vortex beams is found to follow Bessel-Gauss distribution.