When the vortex beam propagates through the turbulent atmosphere, the random variations will be produced in the amplitude and phase of the beam. And the intensity fluctuations and spread of the radiation pattern will be induced at the observation plane. some results about the vortex beams broadening are obtained by numerical modeling using four-dimension code when the vortex beams propagate through the turbulent atmosphere under different conditions. The vortex beams are the lower order Laguerre-Gaussian modes. The results indicate that if the propagation distance is longer or the turbulence is stronger, the beam broadened by the turbulence will be more severe. And if the topological charge is higher, or the beam′s waist width is narrower, or the wavelength is longer, the beam broadened by the turbulence will be smaller. Though the inner scale and the outer scale of turbulence have an effect on the beam broadening, the influence of them is relatively weak. In addition, the broadening of vortex beam and fundamental Gauss beam through the turbulent atmosphere are compared numerically.