The adjacent vertex-distinguishing edge-coloring of a graph $G$ is a proper edge-coloring of $G$ such that each pair of adjacent vetices receives a distinct set of colors. The minimum number of colors required in an adjacent vertex-distinguishing edge-coloring of $G$ is called the adjacent vertex-distinguishing chromatic index. In this paper, we determine the adjacent vertex distinguishing chromatic indices of cubic Halin graphs whose characteristic trees are caterpillars.