In order to study spiral spectrum spread after Laguerre-Gassian (LG) beam propagating through atmospheric turbulence, the method of multiple phase screen is proposed to simulate the transmission of LG beams carrying Orbital Angular Momentum (OAM) in atmospheric turbulence. Propagation of Laguerre-Gaussian beam through atmospheric turbulence is simulated using phase screen based on Fourier transform following the non-Kolmogorov spectrum and the effect induced by atmospheric turbulence is computed quantitatively for different topological charges, wavelengths, exponent parameters, structure constant of the refractive-index fluctuations, inner scales and outer scales. The simulation results show that atmospheric turbulence deteriorates spiral spectrum of LG beam. It is also shown that system performance is closely related to topological charge, wavelength, exponent parameters, structure constant of the refractive-index fluctuations, inner scales and outer scales.