The appearance of wave-front circle edge dislocations and the relationship between the location of the wave-front dislocations of a Gaussian-Shell beam,which was propagating in a weak turbulent atmosphere and in near ground,and the parameters of the turbulent-strength and the distance of propagation had been discussed by the Rytov approximation and the short-term statistical averaging-position of dislocation that was developed in this paper.The relationship between the positions of the wave-front dislocations of the Gaussian-Shell beams propagation in turbulent atmosphere and the atmospheric turbulence strength, the beam propagation distance were analyzed based on a approximation model that the co-axial combined beams and the intersecting combined beams propagated in turbulent atmosphere.The formulas of the statistical average radius of wave-front circle edge dislocations had been developed for the coaxes beams that had different beam diamantes and crossbeams in the cases that the averaging time was shorter t