Abstract: The directional similarity-based robust clustering approach DSCM for directional data is presented in this paper. The DSCM utilizes the objective function based on the directional similarity measure, and then optimizes it using the fixed point iteration method such that all the stable states of the data samples are derived. By presenting all these stable states to the hierarchical clustering algorithm AHC, the final clustering results are obtained. This new approach exhibits its robustness to initialization and capability to reasonably detect the number of clusters for clustering directional data. The experimental results demonstrate its validity and distinctive superiority over the two conventional directional clustering algorithms.