In order to analysis the Gaussian beam transmission characteristics, according to the numerical simulation method of random phase screen, the Rytov weak turbulence theory is used to analyze each statistical quantity. The numerical model of Gaussian beam propagation through an arbitrary thickness phase screen is established, based on the Kolmogorov spectrum, and the analytic expression which is easy to be treated is also given. Meantime, the scintillation index and Rytov variance are analyzed. The results indicate that the application range of arbitrary thickness phase screen model is wider than the thin phase screen, and the statistic describing is more accurate.