This paper studies the propagation of a vortex beam in Bessel lattices, which are produced by optical induction in the focusing photorefractive nonlinear crystal. By numerical simulation, different results are got under different parameters, such as the intensity of the bias electric field on the lattices, the transverse scale coefficient and the deep of the Bessel lattices. These results show that because of existence of the lattices, the input ring vortex beam can overcome the azimuthal modulation instabilities induced by the focusing nonlinearity and form a ring-like vortex soliton which can propagate stably in a quite long distance under appropriate conditions. In addition, the input beam can evolve into a structure of two rings that the big ring surrounds the small one during propagation when the energy of input beam is not just seated in the ring-like channel of the Bessel lattices.