The propagation of Laguerre-Gaussian beam in intermediate fluctuation turbulent atmosphere is studied. Using the split-step Fourier method and the phase screen method, the intensity distribution, phase distribution and the spectrum distribution of LG beam are simulated in the case of up-downlink communications path and level communication path respectively. It is found that the atmospheric turbulence will induce the spread of the spiral spectrum. With the increase of the topological charge and refractive index structure constant, the spectrum spread becomes more serious. It is also concluded that the influence of the atmospheric turbulence on the Laguerre-Gaussian beams is smaller in up-downlink communication path than in level communication path.