In this paper, by using the Rayleigh-Sommer field theory and the cross-spectral density function, theanalytical expression for the intensity distribution of a double half-Gaussian hollow beam in a turbulentatmosphere is obtained. The influence of the initial spot size of this beam on its propagation propertiesin a turbulent atmosphere is simulated, and the intensity distributions for such beams with different spotsizes are obtained. The results show that the initial spot size has an important influence on the propagationproperties in the near field, while this influence in the far field is very weak.