The propagation of vortex beam in atmospheric turbulence is of great importance in theoretical study and practical applications. Based on the Rytov approximation and extended Huygens-Fresnel integral, the analytical expressions for the spiral spectrum of the Laguerre-Gaussian (LG) beam propagating in a slant non-Kolmogorov turbulence channel have been derived and the average capacity of free space optical system is given. The average capaticy of free space optical system is examined and the effects of exponent parameter, wavelength, zenith angle, inner scale, outer scale, and structure constant on average capacity are also analyzed. Results obtained in this paper may be benefical to optical communication.