Scintillation is a highly discussed problem in laser atmospheric transmission, which plays an important role in improving the reliability and performance of laser communication systems. In this study, numerical simulations are conducted using a computational model to investigate the variation of the on-axis scintillation index of the focused platform beam during horizontal atmospheric propagation, considering different transmitter aperture sizes. The simulation results indicate that the aperture size significantly affects the scintillation index. Under the same Rytov variance conditions, larger aperture sizes lead to stronger scintillation effects. For smaller aperture sizes, the scintillation index maintains a relatively linear relationship with the Rytov variance. The findings of this study provide further insights into the factors influencing the scintillation characteristics in laser atmospheric transmission and offer valuable references for the design and engineering applications of laser communication systems.