The multiple random phase screen simulation method is used to simulate the anisotropic turbulent atmosphere and Bessel-Gaussian beam in intensity distribution, the on-axis scintillation and beam wander. The effects of anisotropic turbulence parameters and wave source parameters on the propagation quality of Bessel-Gasuuain beam are analyzed. The results show that the intensity distribution of Bessel-Gaussian beam in anisotropic turbulent atmosphere is related to the off-axis distance. Only the intensity value at the first ring decreases monotonously, while the intensity value at the other secondary rings increases first and then decreases. The on-axis scintillation index of the Bessel-Gaussian beam at close range decreases with the increase of the waveform parameter, and there is a trend of first rising, then falling and then rising with the increase of beam width. This phenomenon is related to the beam width of Bessel-Gaussian beam. The beam wander decreases with increases of the waveform parameter, the number of orbital angular momentum, the wavelength and the beam width. However, at a long distance, its on-axis scintillation index and beam wander effect are opposite to that of near distance, which is consistent with the sudden increase of the width of Bessel-Gaussian beam. The wander effect of Bessel-Gaussian beam in anisotropic turbulent atmosphere is significantly less than that in isotropic turbulence atmosphere, and the result even larger than Laguerre-Gaussian beam at long distance.