Clustering methods have been widely applied in various areas. The objective of clustering is to find the data structure and also to partition the data set into groups with similar individuals. A mean shift-based method had been proposed as a clustering algorithm. However, most mean shift-based clustering algorithms are used for numeric data. In this paper, we propose a mean shift-based clustering algorithm for directional data. The clustering algorithm gives us a new way in the analysis of grouped directional data on the plane. Some numerical examples are given to demonstrate its effectiveness and superiority.