The intensity distribution and the wander of optical vortices of Laguerre-Gaussian beams propagating in turbulent atmosphere are simulated numerically. The results indicate that intensity profiles of vortex beams experienced successive variation from annular structures to flattened-top profiles and finally to Gaussian profiles with the propagation. The variation is closely related with the propagation distance, the turbulence strength, the outer scale of turbulence, the number of topological charge, the width of beam waist and the wavelength of vortex beam. However, the variation is nothing to do with the inner scale of turbulence. The wandering behavior of optical vortices in the atmosphere is described by the occurrence number on a transverse plane. The results show that the occurrence number on the receiver plane follows Gaussian statistics. As the propagation distance, the turbulence strength, or the topological charge of the vortex beam increases, the Gaussian fitting curves become broader, and the statistics of vortex position tends to random distribution. In addition, choosing the suitable width of the vortex beam waist can reduce the wander of optical vortices.