Average channel capacity of free space optical (FSO) communication systems using a Gaussian beam with the intensity modulation and direct detection technique is investigated in anisotropic non-Kolmogorov strong turbulent atmosphere. The channel model is selected as gamma-gamma distribution, which is valid for strong turbulence. Obtained results show that anisotropy in both the horizontal and vertical affects the average channel capacity of an FSO communication system positively. Average channel capacity increases with the increase of photodetector quantum efficiency, wavelength, Gaussian beam source size, inner scale length, and non-Kolmogorov power law exponent. An increase of link length, turbulence structure constant, and noise variance causes a decrease in average channel capacity. The average channel capacity falls very little with the increase of outer scale length.