Vortex beam arrays have gradually gained attention because of their potential applications in high-power laser synthesis, space optical communication, and laser engineering. Based on a numerical method, namely, the multiple phase screen method, we study the propagation characteristics of a vortex beam array in von Karman turbulence and analyze the light field evolution. The results indicate that the light beam is fused after transmission over a certain distance, and the topological charge of the fused beam is the same as that of the sub-beam in the initial light field. Considering that the expansion of the spot will lead to a loss of topological charge, thereby reducing the communication efficiency, we analyze the influences of various turbulence and beam parameters on the relative beam radius. Among these parameters, turbulence intensity has a great influence on relative beam width, and the other parameters such as topological charge have different degrees of impact. The relative beam radius of the vortex beam array is smaller than that of the single vortex beam.