The Cameron-Praeger conjecture stands as a central problem at the intersection of group theory and combinatorial design, and has inspired sustained research by mathematicians worldwide for decades. In this paper, we took a step forward in the proof of the Cameron-Praeger conjecture. We studied a special case of the famous Cameron-Praeger conjecture in design theory and proved that there are no block-transitive $6$- $(v,k,2)$ designs with $k$ dividing $v$.