Based on the extended HuygensFresnel integral, the analytic expressions for BesselGaussian beams (BGBs) with optical vortices propagating in turbulent atmosphere are derived. The average intensity properties and the beam quality (Power in bucket) in the far field of BesselGaussian beams with optical vortices propagating in turbulent atmosphere are investigated. It is found that intensity profiles of BesselGaussian beams experienced successive variations and the phase singularity rapidly fades away during propagating in turbulent atmosphere. The process is closely related with the number of topological charge, the beam′s waist width and the strength of atmospheric turbulence. The maintenance of singularity of vortex beams with larger topological charge in turbulent atmosphere is better than that for vortex beams with smaller topological charge. In addition, based on the theory of power in bucket, the influence of topological charge, the beam′s waist width and the strength of atmospheric turbulence on the beam quality of BesselGaussian beams is explored in detail.