Taking the Bessel and Bessel-Gauss vortex beams shaped by a circular aperture as examples, beam spreading and phase singularities' behavior of approximate non-diffracting vortex beams in turbulent atmosphere are numerically simulated. The simulation results show that, the spreading of Bessel-Gauss vortex beam caused by the atmospheric turbulence is less than that of the Bessel vortex beam, and the algebraic sum of the phase singularities of Bessel-Gauss vortex beams remains close to the topological charges of the input vortex beams. In addition, the algebraic sum fluctuation deviation of the phase singularities of Bessel-Gauss vortex beams is smaller than that of Bessel vortex beams in long distance propagation. As the information carrier, Bessel-Gauss vortex beams have potential application in free space optical communication.