An analysis of the propagation of Laguerre-Gaussian beam in fluctuation turbulent atmosphere is performed. Under the Rytov approximation, the integral expression of the spiral spectrum of the beam at the receiver aperture is obtained. It is found that the atmospheric turbulence will induce the spread of the spiral spectrum. With increasing topological charge, propagation distance, refractive index structure constant and radius of receiver aperture, the spectrum spread becomes more serious. It is also shown that the dimensionless variance describing the degree of the spread is a quadratic function of the refractive index structure constant and the radius of receiver aperture respectively, while it is an 11th order function of the topological charge and a 6th order function of the propagation distance. The analytical expression of the spiral spectrum is derived by taking account of the simulation results that both radial index and waist radius have little effect on the spiral spectrum.