Light intensity fluctuation is caused by atmospheric turbulence while laser beam travels in atmosphere. In order to find an approach to weaken or remove the effect of turbulence, the influence of atmospheric turbulence on the axial intensity of Bessel-Gauss Beams of zero-order was investigated by means of numerical simulation. The results show that the axial intensity of Bessel-Gauss beams decreases with the increase of propagation distance, and the stronger the atmospheric turbulence is, the faster the axial intensity decreases. The smaller the radial wave vectors of the Bessel-Gauss beams of zero-order, the better the stability of their axial intensity. The stability of axial intensity of Bessel-Gauss beams gets worse with the increase of propagation distance. Compared with Gaussian beams with the same beam width, the axial intensity of Bessel-Gauss beams is more affected by atmospheric turbulence.