Aiming at the problem that the research scene of multi Bessel Gaussian beam distorted wavefront correction under atmospheric turbulence interference is single, a multi Bessel Gaussian beam distorted wavefront correction method based on Gasberg Sexton（GS） algorithm is proposed, and the anisotropic turbulence phase screen is obtained by using the power spectrum inversion method. The distorted wavefront correction of two kinds of multi Bessel Gaussian beam with different sign topology and the same sign topology under the influence of three different atmospheric turbulence refractive index structure constants is simulated and analyzed. The simulation results show that the purity of the target orbital angular momentum（OAM） mode of the two kinds of multi Bessel Gaussian beam after correction can be improved by more than 12%, and the dispersion of OAM spectrum can also be effectively suppressed.