Abstract: The propagation of a focused Gaussian beam through turbulent atmosphere is simulated by using non-adaptive coordinate transformation. The first-order weak-fluctuation Rytov theory predicts that the on-axis scintillation index would become significantly smaller as the initial beam width increases. But the simulation results show that there is no great reduction of on-axis scintillation index. This discrepancy is due to the fact that Rytov theory does not correctly account for the effects of beam wander caused by large scale turbulence. Simulation results are in good agreement with beam wander theory results and experimental data. It can be concluded that Rytov theory could not correctly calculate the scintillation index of a focused beam and the effects of beam wander should be taken into a