A laser beam with a different irradiance profile may have favorable scintillation and diffraction characteristics, which are important qualities in the area of optical wireless communication. The propagation in random media (atmosphere) of a laser beam with an annular, donut-shaped, irradiance cross section was examined. Annular beams are created by unstable optical resonators, which are used as resonant cavities in high power lasers, and by beam expanders that consist of telescopes where the second mirror obstruct the central portion of the circular aperture. The annular beam was modeled as the difference of two collimated Gaussian beams, with different spot sizes. Diffraction and scintillation characteristics of the annular beam, for horizontal near ground propagation (i.e. constant refractive-index structure parameter Cn2), were compared to one collimated and one focused Gaussian beam. The Rytov approximation was used to calculate the on-axis scintillation index in weak atmospheric turbulence for both the annular and the Gaussian beams. The extended Huygens-Fresnel integral was solved to obtain the mean irradiance, from which the fraction of power in half aperture diameter was calculated.