Free-space laser system performance is limited by atmospheric turbulence that has been described for many years by Kolmogorov’s power spectral density model because of its simplicity. However, many inland and overseas experiments concerning non-Kolmogorov atmospheric turbulence have showed recently that Kolmogorov’s theory is sometimes imcomplete to describe atmospheric turbulence statistics correctly, in particular in portions of the troposphere and stratosphere. It is the first problem to investigate the effect of non-Kolmogorov on the propagation of light in order to know completely the effect of atmospheric turbulence on free-space laser communications. In this paper using the non-Kolmogorov turbulent power spectral density, we derived the variances of beam wander of the convergent and collimated beams, which are analytic and concise, and then analyzed the formulas.